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\\end{pmatrix}.",[573,912,914,979],{"className":913,"ariaHidden":615},[614],[573,915,917,920,923,926,929,932,935,970,973,976],{"className":916},[619],[573,918],{"className":919,"style":624},[623],[573,921,594],{"className":922,"style":630},[628,629],[573,924,599],{"className":925},[634],[573,927,602],{"className":928},[628,629],[573,930,605],{"className":931},[641],[573,933],{"className":934,"style":787},[756],[573,936,938],{"className":937},[628,700],[573,939,941],{"className":940},[704],[573,942,944],{"className":943},[708],[573,945,947,955],{"className":946,"style":696},[712],[573,948,949,952],{"style":715},[573,950],{"className":951,"style":720},[719],[573,953,660],{"className":954,"style":724},[628,629],[573,956,957,960],{"style":715},[573,958],{"className":959,"style":720},[719],[573,961,963],{"className":962,"style":734},[733],[573,964,966],{"className":965,"style":739},[738],[741,967,968],{"xmlns":743,"width":744,"height":745,"style":746,"viewBox":747,"preserveAspectRatio":748},[750,969],{"d":752},[573,971],{"className":972,"style":757},[756],[573,974,666],{"className":975},[761],[573,977],{"className":978,"style":757},[756],[573,980,982,986,1140,1143],{"className":981},[619],[573,983],{"className":984,"style":985},[623],"height:2.4em;vertical-align:-0.95em;",[573,987,990,1000,1134],{"className":988},[989],"minner",[573,991,995],{"className":992,"style":994},[634,993],"delimcenter","top:0em;",[573,996,599],{"className":997},[998,999],"delimsizing","size3",[573,1001,1003],{"className":1002},[628],[573,1004,1006],{"className":1005},[836],[573,1007,1010],{"className":1008},[1009],"col-align-c",[573,1011,1014,1125],{"className":1012},[704,1013],"vlist-t2",[573,1015,1017,1120],{"className":1016},[708],[573,1018,1021,1072],{"className":1019,"style":1020},[712],"height:1.45em;",[573,1022,1024,1027],{"style":1023},"top:-3.61em;",[573,1025],{"className":1026,"style":720},[719],[573,1028,1030,1033,1036,1040,1043,1046,1050,1054,1057,1060,1063,1066,1069],{"className":1029},[628],[573,1031,671],{"className":1032},[628,629],[573,1034],{"className":1035,"style":787},[756],[573,1037,857],{"className":1038},[1039],"mop",[573,1041],{"className":1042,"style":787},[756],[573,1044,602],{"className":1045},[628,629],[573,1047],{"className":1048,"style":1049},[756],"margin-right:0.2222em;",[573,1051,865],{"className":1052},[1053],"mbin",[573,1055],{"className":1056,"style":1049},[756],[573,1058,681],{"className":1059,"style":724},[628,629],[573,1061],{"className":1062,"style":787},[756],[573,1064,870],{"className":1065},[1039],[573,1067],{"className":1068,"style":787},[756],[573,1070,602],{"className":1071},[628,629],[573,1073,1075,1078],{"style":1074},"top:-2.41em;",[573,1076],{"className":1077,"style":720},[719],[573,1079,1081,1084,1087,1090,1093,1096,1099,1102,1105,1108,1111,1114,1117],{"className":1080},[628],[573,1082,671],{"className":1083},[628,629],[573,1085],{"className":1086,"style":787},[756],[573,1088,870],{"className":1089},[1039],[573,1091],{"className":1092,"style":787},[756],[573,1094,602],{"className":1095},[628,629],[573,1097],{"className":1098,"style":1049},[756],[573,1100,893],{"className":1101},[1053],[573,1103],{"className":1104,"style":1049},[756],[573,1106,681],{"className":1107,"style":724},[628,629],[573,1109],{"className":1110,"style":787},[756],[573,1112,857],{"className":1113},[1039],[573,1115],{"className":1116,"style":787},[756],[573,1118,602],{"className":1119},[628,629],[573,1121,1124],{"className":1122},[1123],"vlist-s","​",[573,1126,1128],{"className":1127},[708],[573,1129,1132],{"className":1130,"style":1131},[712],"height:0.95em;",[573,1133],{},[573,1135,1137],{"className":1136,"style":994},[641,993],[573,1138,605],{"className":1139},[998,999],[573,1141],{"className":1142,"style":787},[756],[573,1144,907],{"className":1145},[628],[564,1147,1148,1149,1152],{},"Ein positiver Winkel dreht ",[568,1150,1151],{},"gegen den Uhrzeigersinn",", ein negativer im Uhrzeigersinn.",[564,1154,1155,1156,1215,1216,1293,1294,1351,1352,907],{},"Die Spalten der Matrix kann man sich gut merken: Die erste Spalte ist das Bild von ",[573,1157,1159,1185],{"className":1158},[576],[573,1160,1162],{"className":1161},[580],[582,1163,1164],{"xmlns":584},[586,1165,1166,1182],{},[589,1167,1168,1170,1174,1176,1178,1180],{},[596,1169,599],{"stretchy":598},[1171,1172,1173],"mn",{},"1",[596,1175,674],{"separator":615},[676,1177,678],{},[1171,1179,850],{},[596,1181,605],{"stretchy":598},[607,1183,1184],{"encoding":609},"(1,\\ 0)",[573,1186,1188],{"className":1187,"ariaHidden":615},[614],[573,1189,1191,1194,1197,1200,1203,1206,1209,1212],{"className":1190},[619],[573,1192],{"className":1193,"style":624},[623],[573,1195,599],{"className":1196},[634],[573,1198,1173],{"className":1199},[628],[573,1201,674],{"className":1202},[780],[573,1204,678],{"className":1205},[756],[573,1207],{"className":1208,"style":787},[756],[573,1210,850],{"className":1211},[628],[573,1213,605],{"className":1214},[641],", also der Punkt ",[573,1217,1219,1251],{"className":1218},[576],[573,1220,1222],{"className":1221},[580],[582,1223,1224],{"xmlns":584},[586,1225,1226,1248],{},[589,1227,1228,1230,1232,1234,1236,1238,1240,1242,1244,1246],{},[596,1229,599],{"stretchy":598},[592,1231,857],{},[596,1233,860],{},[592,1235,602],{},[596,1237,674],{"separator":615},[676,1239,678],{},[592,1241,870],{},[596,1243,860],{},[592,1245,602],{},[596,1247,605],{"stretchy":598},[607,1249,1250],{"encoding":609},"(\\cos\\varphi,\\ \\sin\\varphi)",[573,1252,1254],{"className":1253,"ariaHidden":615},[614],[573,1255,1257,1260,1263,1266,1269,1272,1275,1278,1281,1284,1287,1290],{"className":1256},[619],[573,1258],{"className":1259,"style":624},[623],[573,1261,599],{"className":1262},[634],[573,1264,857],{"className":1265},[1039],[573,1267],{"className":1268,"style":787},[756],[573,1270,602],{"className":1271},[628,629],[573,1273,674],{"className":1274},[780],[573,1276,678],{"className":1277},[756],[573,1279],{"className":1280,"style":787},[756],[573,1282,870],{"className":1283},[1039],[573,1285],{"className":1286,"style":787},[756],[573,1288,602],{"className":1289},[628,629],[573,1291,605],{"className":1292},[641]," auf dem Einheitskreis. Die zweite Spalte ist das Bild von ",[573,1295,1297,1321],{"className":1296},[576],[573,1298,1300],{"className":1299},[580],[582,1301,1302],{"xmlns":584},[586,1303,1304,1318],{},[589,1305,1306,1308,1310,1312,1314,1316],{},[596,1307,599],{"stretchy":598},[1171,1309,850],{},[596,1311,674],{"separator":615},[676,1313,678],{},[1171,1315,1173],{},[596,1317,605],{"stretchy":598},[607,1319,1320],{"encoding":609},"(0,\\ 1)",[573,1322,1324],{"className":1323,"ariaHidden":615},[614],[573,1325,1327,1330,1333,1336,1339,1342,1345,1348],{"className":1326},[619],[573,1328],{"className":1329,"style":624},[623],[573,1331,599],{"className":1332},[634],[573,1334,850],{"className":1335},[628],[573,1337,674],{"className":1338},[780],[573,1340,678],{"className":1341},[756],[573,1343],{"className":1344,"style":787},[756],[573,1346,1173],{"className":1347},[628],[573,1349,605],{"className":1350},[641],", also ",[573,1353,1355,1389],{"className":1354},[576],[573,1356,1358],{"className":1357},[580],[582,1359,1360],{"xmlns":584},[586,1361,1362,1386],{},[589,1363,1364,1366,1368,1370,1372,1374,1376,1378,1380,1382,1384],{},[596,1365,599],{"stretchy":598},[596,1367,865],{},[592,1369,870],{},[596,1371,860],{},[592,1373,602],{},[596,1375,674],{"separator":615},[676,1377,678],{},[592,1379,857],{},[596,1381,860],{},[592,1383,602],{},[596,1385,605],{"stretchy":598},[607,1387,1388],{"encoding":609},"(-\\sin\\varphi,\\ \\cos\\varphi)",[573,1390,1392],{"className":1391,"ariaHidden":615},[614],[573,1393,1395,1398,1401,1404,1407,1410,1413,1416,1419,1422,1425,1428,1431,1434],{"className":1394},[619],[573,1396],{"className":1397,"style":624},[623],[573,1399,599],{"className":1400},[634],[573,1402,865],{"className":1403},[628],[573,1405],{"className":1406,"style":787},[756],[573,1408,870],{"className":1409},[1039],[573,1411],{"className":1412,"style":787},[756],[573,1414,602],{"className":1415},[628,629],[573,1417,674],{"className":1418},[780],[573,1420,678],{"className":1421},[756],[573,1423],{"className":1424,"style":787},[756],[573,1426,857],{"className":1427},[1039],[573,1429],{"className":1430,"style":787},[756],[573,1432,602],{"className":1433},[628,629],[573,1435,605],{"className":1436},[641],[564,1438,1439],{},"Eigenschaften:",[1441,1442,1443,1447,1582,1678],"ul",{},[1444,1445,1446],"li",{},"Eine Drehung ändert keine Längen und keine Winkel.",[1444,1448,1449,1450,907],{},"Zwei Drehungen hintereinander ergeben eine Drehung um die Summe der Winkel: ",[573,1451,1453,1499],{"className":1452},[576],[573,1454,1456],{"className":1455},[580],[582,1457,1458],{"xmlns":584},[586,1459,1460,1496],{},[589,1461,1462,1464,1466,1469,1471,1473,1475,1477,1480,1482,1484,1486,1488,1490,1492,1494],{},[592,1463,594],{},[596,1465,599],{"stretchy":598},[592,1467,1468],{},"α",[596,1470,605],{"stretchy":598},[676,1472,822],{},[592,1474,594],{},[596,1476,599],{"stretchy":598},[592,1478,1479],{},"β",[596,1481,605],{"stretchy":598},[596,1483,666],{},[592,1485,594],{},[596,1487,599],{"stretchy":598},[592,1489,1468],{},[596,1491,893],{},[592,1493,1479],{},[596,1495,605],{"stretchy":598},[607,1497,1498],{"encoding":609},"R(\\alpha)\\,R(\\beta) = R(\\alpha + \\beta)",[573,1500,1502,1546,1570],{"className":1501,"ariaHidden":615},[614],[573,1503,1505,1508,1511,1514,1518,1521,1524,1527,1530,1534,1537,1540,1543],{"className":1504},[619],[573,1506],{"className":1507,"style":624},[623],[573,1509,594],{"className":1510,"style":630},[628,629],[573,1512,599],{"className":1513},[634],[573,1515,1468],{"className":1516,"style":1517},[628,629],"margin-right:0.0037em;",[573,1519,605],{"className":1520},[641],[573,1522],{"className":1523,"style":787},[756],[573,1525,594],{"className":1526,"style":630},[628,629],[573,1528,599],{"className":1529},[634],[573,1531,1479],{"className":1532,"style":1533},[628,629],"margin-right:0.0528em;",[573,1535,605],{"className":1536},[641],[573,1538],{"className":1539,"style":757},[756],[573,1541,666],{"className":1542},[761],[573,1544],{"className":1545,"style":757},[756],[573,1547,1549,1552,1555,1558,1561,1564,1567],{"className":1548},[619],[573,1550],{"className":1551,"style":624},[623],[573,1553,594],{"className":1554,"style":630},[628,629],[573,1556,599],{"className":1557},[634],[573,1559,1468],{"className":1560,"style":1517},[628,629],[573,1562],{"className":1563,"style":1049},[756],[573,1565,893],{"className":1566},[1053],[573,1568],{"className":1569,"style":1049},[756],[573,1571,1573,1576,1579],{"className":1572},[619],[573,1574],{"className":1575,"style":624},[623],[573,1577,1479],{"className":1578,"style":1533},[628,629],[573,1580,605],{"className":1581},[641],[1444,1583,1584,1585,1634,1635,907],{},"Die Rückdrehung ist ",[573,1586,1588,1610],{"className":1587},[576],[573,1589,1591],{"className":1590},[580],[582,1592,1593],{"xmlns":584},[586,1594,1595,1607],{},[589,1596,1597,1599,1601,1603,1605],{},[592,1598,594],{},[596,1600,599],{"stretchy":598},[596,1602,865],{},[592,1604,602],{},[596,1606,605],{"stretchy":598},[607,1608,1609],{"encoding":609},"R(-\\varphi)",[573,1611,1613],{"className":1612,"ariaHidden":615},[614],[573,1614,1616,1619,1622,1625,1628,1631],{"className":1615},[619],[573,1617],{"className":1618,"style":624},[623],[573,1620,594],{"className":1621,"style":630},[628,629],[573,1623,599],{"className":1624},[634],[573,1626,865],{"className":1627},[628],[573,1629,602],{"className":1630},[628,629],[573,1632,605],{"className":1633},[641],", das ist zugleich die Transponierte von ",[573,1636,1638,1657],{"className":1637},[576],[573,1639,1641],{"className":1640},[580],[582,1642,1643],{"xmlns":584},[586,1644,1645,1655],{},[589,1646,1647,1649,1651,1653],{},[592,1648,594],{},[596,1650,599],{"stretchy":598},[592,1652,602],{},[596,1654,605],{"stretchy":598},[607,1656,610],{"encoding":609},[573,1658,1660],{"className":1659,"ariaHidden":615},[614],[573,1661,1663,1666,1669,1672,1675],{"className":1662},[619],[573,1664],{"className":1665,"style":624},[623],[573,1667,594],{"className":1668,"style":630},[628,629],[573,1670,599],{"className":1671},[634],[573,1673,602],{"className":1674},[628,629],[573,1676,605],{"className":1677},[641],[1444,1679,1680,907],{},[573,1681,1683,1742],{"className":1682},[576],[573,1684,1686],{"className":1685},[580],[582,1687,1688],{"xmlns":584},[586,1689,1690,1739],{},[589,1691,1692,1695,1697,1699,1701,1703,1705,1707,1719,1721,1723,1733,1735,1737],{},[592,1693,1694],{},"det",[596,1696,860],{},[592,1698,594],{},[596,1700,599],{"stretchy":598},[592,1702,602],{},[596,1704,605],{"stretchy":598},[596,1706,666],{},[1708,1709,1710,1716],"msup",{},[589,1711,1712,1714],{},[592,1713,857],{},[596,1715,860],{},[1171,1717,1718],{},"2",[592,1720,602],{},[596,1722,893],{},[1708,1724,1725,1731],{},[589,1726,1727,1729],{},[592,1728,870],{},[596,1730,860],{},[1171,1732,1718],{},[592,1734,602],{},[596,1736,666],{},[1171,1738,1173],{},[607,1740,1741],{"encoding":609},"\\det R(\\varphi) = \\cos^2\\varphi + \\sin^2\\varphi = 1",[573,1743,1745,1778,1836,1889],{"className":1744,"ariaHidden":615},[614],[573,1746,1748,1751,1754,1757,1760,1763,1766,1769,1772,1775],{"className":1747},[619],[573,1749],{"className":1750,"style":624},[623],[573,1752,1694],{"className":1753},[1039],[573,1755],{"className":1756,"style":787},[756],[573,1758,594],{"className":1759,"style":630},[628,629],[573,1761,599],{"className":1762},[634],[573,1764,602],{"className":1765},[628,629],[573,1767,605],{"className":1768},[641],[573,1770],{"className":1771,"style":757},[756],[573,1773,666],{"className":1774},[761],[573,1776],{"className":1777,"style":757},[756],[573,1779,1781,1785,1821,1824,1827,1830,1833],{"className":1780},[619],[573,1782],{"className":1783,"style":1784},[623],"height:1.0085em;vertical-align:-0.1944em;",[573,1786,1788,1791],{"className":1787},[1039],[573,1789,857],{"className":1790},[1039],[573,1792,1795],{"className":1793},[1794],"msupsub",[573,1796,1798],{"className":1797},[704],[573,1799,1801],{"className":1800},[708],[573,1802,1805],{"className":1803,"style":1804},[712],"height:0.8141em;",[573,1806,1808,1812],{"style":1807},"top:-3.063em;margin-right:0.05em;",[573,1809],{"className":1810,"style":1811},[719],"height:2.7em;",[573,1813,1818],{"className":1814},[1815,1816,999,1817],"sizing","reset-size6","mtight",[573,1819,1718],{"className":1820},[628,1817],[573,1822],{"className":1823,"style":787},[756],[573,1825,602],{"className":1826},[628,629],[573,1828],{"className":1829,"style":1049},[756],[573,1831,893],{"className":1832},[1053],[573,1834],{"className":1835,"style":1049},[756],[573,1837,1839,1843,1874,1877,1880,1883,1886],{"className":1838},[619],[573,1840],{"className":1841,"style":1842},[623],"height:1.0663em;vertical-align:-0.1944em;",[573,1844,1846,1849],{"className":1845},[1039],[573,1847,870],{"className":1848},[1039],[573,1850,1852],{"className":1851},[1794],[573,1853,1855],{"className":1854},[704],[573,1856,1858],{"className":1857},[708],[573,1859,1862],{"className":1860,"style":1861},[712],"height:0.8719em;",[573,1863,1865,1868],{"style":1864},"top:-3.1208em;margin-right:0.05em;",[573,1866],{"className":1867,"style":1811},[719],[573,1869,1871],{"className":1870},[1815,1816,999,1817],[573,1872,1718],{"className":1873},[628,1817],[573,1875],{"className":1876,"style":787},[756],[573,1878,602],{"className":1879},[628,629],[573,1881],{"className":1882,"style":757},[756],[573,1884,666],{"className":1885},[761],[573,1887],{"className":1888,"style":757},[756],[573,1890,1892,1896],{"className":1891},[619],[573,1893],{"className":1894,"style":1895},[623],"height:0.6444em;",[573,1897,1173],{"className":1898},[628],[564,1900,1901,1902,1933,1934,1962],{},"Soll um einen anderen Punkt ",[573,1903,1905,1919],{"className":1904},[576],[573,1906,1908],{"className":1907},[580],[582,1909,1910],{"xmlns":584},[586,1911,1912,1917],{},[589,1913,1914],{},[592,1915,1916],{},"Z",[607,1918,1916],{"encoding":609},[573,1920,1922],{"className":1921,"ariaHidden":615},[614],[573,1923,1925,1929],{"className":1924},[619],[573,1926],{"className":1927,"style":1928},[623],"height:0.6833em;",[573,1930,1916],{"className":1931,"style":1932},[628,629],"margin-right:0.0715em;"," gedreht werden, verschiebt man zuerst ",[573,1935,1937,1950],{"className":1936},[576],[573,1938,1940],{"className":1939},[580],[582,1941,1942],{"xmlns":584},[586,1943,1944,1948],{},[589,1945,1946],{},[592,1947,1916],{},[607,1949,1916],{"encoding":609},[573,1951,1953],{"className":1952,"ariaHidden":615},[614],[573,1954,1956,1959],{"className":1955},[619],[573,1957],{"className":1958,"style":1928},[623],[573,1960,1916],{"className":1961,"style":1932},[628,629]," in den Ursprung, dreht und verschiebt zurück.",[559,1964,1966],{"id":1965},"beispiele","Beispiele",[564,1968,1969,1970,2027,2028,2094,2095,2189,2190,2284,2285,907],{},"Der Vektor ",[573,1971,1973,1997],{"className":1972},[576],[573,1974,1976],{"className":1975},[580],[582,1977,1978],{"xmlns":584},[586,1979,1980,1994],{},[589,1981,1982,1984,1986,1988,1990,1992],{},[596,1983,599],{"stretchy":598},[1171,1985,1718],{},[596,1987,674],{"separator":615},[676,1989,678],{},[1171,1991,1173],{},[596,1993,605],{"stretchy":598},[607,1995,1996],{"encoding":609},"(2,\\ 1)",[573,1998,2000],{"className":1999,"ariaHidden":615},[614],[573,2001,2003,2006,2009,2012,2015,2018,2021,2024],{"className":2002},[619],[573,2004],{"className":2005,"style":624},[623],[573,2007,599],{"className":2008},[634],[573,2010,1718],{"className":2011},[628],[573,2013,674],{"className":2014},[780],[573,2016,678],{"className":2017},[756],[573,2019],{"className":2020,"style":787},[756],[573,2022,1173],{"className":2023},[628],[573,2025,605],{"className":2026},[641]," wird um ",[573,2029,2031,2051],{"className":2030},[576],[573,2032,2034],{"className":2033},[580],[582,2035,2036],{"xmlns":584},[586,2037,2038,2048],{},[589,2039,2040],{},[1708,2041,2042,2045],{},[1171,2043,2044],{},"90",[596,2046,2047],{},"∘",[607,2049,2050],{"encoding":609},"90^\\circ",[573,2052,2054],{"className":2053,"ariaHidden":615},[614],[573,2055,2057,2061,2065],{"className":2056},[619],[573,2058],{"className":2059,"style":2060},[623],"height:0.6741em;",[573,2062,2064],{"className":2063},[628],"9",[573,2066,2068,2071],{"className":2067},[628],[573,2069,850],{"className":2070},[628],[573,2072,2074],{"className":2073},[1794],[573,2075,2077],{"className":2076},[704],[573,2078,2080],{"className":2079},[708],[573,2081,2083],{"className":2082,"style":2060},[712],[573,2084,2085,2088],{"style":1807},[573,2086],{"className":2087,"style":1811},[719],[573,2089,2091],{"className":2090},[1815,1816,999,1817],[573,2092,2047],{"className":2093},[1053,1817]," gedreht. Mit ",[573,2096,2098,2124],{"className":2097},[576],[573,2099,2101],{"className":2100},[580],[582,2102,2103],{"xmlns":584},[586,2104,2105,2121],{},[589,2106,2107,2109,2111,2117,2119],{},[592,2108,857],{},[596,2110,860],{},[1708,2112,2113,2115],{},[1171,2114,2044],{},[596,2116,2047],{},[596,2118,666],{},[1171,2120,850],{},[607,2122,2123],{"encoding":609},"\\cos 90^\\circ = 0",[573,2125,2127,2180],{"className":2126,"ariaHidden":615},[614],[573,2128,2130,2133,2136,2139,2142,2171,2174,2177],{"className":2129},[619],[573,2131],{"className":2132,"style":2060},[623],[573,2134,857],{"className":2135},[1039],[573,2137],{"className":2138,"style":787},[756],[573,2140,2064],{"className":2141},[628],[573,2143,2145,2148],{"className":2144},[628],[573,2146,850],{"className":2147},[628],[573,2149,2151],{"className":2150},[1794],[573,2152,2154],{"className":2153},[704],[573,2155,2157],{"className":2156},[708],[573,2158,2160],{"className":2159,"style":2060},[712],[573,2161,2162,2165],{"style":1807},[573,2163],{"className":2164,"style":1811},[719],[573,2166,2168],{"className":2167},[1815,1816,999,1817],[573,2169,2047],{"className":2170},[1053,1817],[573,2172],{"className":2173,"style":757},[756],[573,2175,666],{"className":2176},[761],[573,2178],{"className":2179,"style":757},[756],[573,2181,2183,2186],{"className":2182},[619],[573,2184],{"className":2185,"style":1895},[623],[573,2187,850],{"className":2188},[628]," und ",[573,2191,2193,2219],{"className":2192},[576],[573,2194,2196],{"className":2195},[580],[582,2197,2198],{"xmlns":584},[586,2199,2200,2216],{},[589,2201,2202,2204,2206,2212,2214],{},[592,2203,870],{},[596,2205,860],{},[1708,2207,2208,2210],{},[1171,2209,2044],{},[596,2211,2047],{},[596,2213,666],{},[1171,2215,1173],{},[607,2217,2218],{"encoding":609},"\\sin 90^\\circ = 1",[573,2220,2222,2275],{"className":2221,"ariaHidden":615},[614],[573,2223,2225,2228,2231,2234,2237,2266,2269,2272],{"className":2224},[619],[573,2226],{"className":2227,"style":2060},[623],[573,2229,870],{"className":2230},[1039],[573,2232],{"className":2233,"style":787},[756],[573,2235,2064],{"className":2236},[628],[573,2238,2240,2243],{"className":2239},[628],[573,2241,850],{"className":2242},[628],[573,2244,2246],{"className":2245},[1794],[573,2247,2249],{"className":2248},[704],[573,2250,2252],{"className":2251},[708],[573,2253,2255],{"className":2254,"style":2060},[712],[573,2256,2257,2260],{"style":1807},[573,2258],{"className":2259,"style":1811},[719],[573,2261,2263],{"className":2262},[1815,1816,999,1817],[573,2264,2047],{"className":2265},[1053,1817],[573,2267],{"className":2268,"style":757},[756],[573,2270,666],{"className":2271},[761],[573,2273],{"className":2274,"style":757},[756],[573,2276,2278,2281],{"className":2277},[619],[573,2279],{"className":2280,"style":1895},[623],[573,2282,1173],{"className":2283},[628]," ergibt sich ",[573,2286,2288,2353],{"className":2287},[576],[573,2289,2291],{"className":2290},[580],[582,2292,2293],{"xmlns":584},[586,2294,2295,2350],{},[589,2296,2297,2299,2301,2304,2306,2308,2310,2312,2314,2316,2318,2320,2322,2324,2326,2328,2330,2332,2334,2336,2338,2340,2342,2344,2346,2348],{},[596,2298,599],{"stretchy":598},[1171,2300,1718],{},[596,2302,2303],{},"⋅",[1171,2305,850],{},[596,2307,865],{},[1171,2309,1173],{},[596,2311,2303],{},[1171,2313,1173],{},[596,2315,674],{"separator":615},[676,2317,678],{},[1171,2319,1718],{},[596,2321,2303],{},[1171,2323,1173],{},[596,2325,893],{},[1171,2327,1173],{},[596,2329,2303],{},[1171,2331,850],{},[596,2333,605],{"stretchy":598},[596,2335,666],{},[596,2337,599],{"stretchy":598},[596,2339,865],{},[1171,2341,1173],{},[596,2343,674],{"separator":615},[676,2345,678],{},[1171,2347,1718],{},[596,2349,605],{"stretchy":598},[607,2351,2352],{"encoding":609},"(2 \\cdot 0 - 1 \\cdot 1,\\ 2 \\cdot 1 + 1 \\cdot 0) = (-1,\\ 2)",[573,2354,2356,2377,2396,2414,2445,2463,2481,2502],{"className":2355,"ariaHidden":615},[614],[573,2357,2359,2362,2365,2368,2371,2374],{"className":2358},[619],[573,2360],{"className":2361,"style":624},[623],[573,2363,599],{"className":2364},[634],[573,2366,1718],{"className":2367},[628],[573,2369],{"className":2370,"style":1049},[756],[573,2372,2303],{"className":2373},[1053],[573,2375],{"className":2376,"style":1049},[756],[573,2378,2380,2384,2387,2390,2393],{"className":2379},[619],[573,2381],{"className":2382,"style":2383},[623],"height:0.7278em;vertical-align:-0.0833em;",[573,2385,850],{"className":2386},[628],[573,2388],{"className":2389,"style":1049},[756],[573,2391,865],{"className":2392},[1053],[573,2394],{"className":2395,"style":1049},[756],[573,2397,2399,2402,2405,2408,2411],{"className":2398},[619],[573,2400],{"className":2401,"style":1895},[623],[573,2403,1173],{"className":2404},[628],[573,2406],{"className":2407,"style":1049},[756],[573,2409,2303],{"className":2410},[1053],[573,2412],{"className":2413,"style":1049},[756],[573,2415,2417,2421,2424,2427,2430,2433,2436,2439,2442],{"className":2416},[619],[573,2418],{"className":2419,"style":2420},[623],"height:0.8389em;vertical-align:-0.1944em;",[573,2422,1173],{"className":2423},[628],[573,2425,674],{"className":2426},[780],[573,2428,678],{"className":2429},[756],[573,2431],{"className":2432,"style":787},[756],[573,2434,1718],{"className":2435},[628],[573,2437],{"className":2438,"style":1049},[756],[573,2440,2303],{"className":2441},[1053],[573,2443],{"className":2444,"style":1049},[756],[573,2446,2448,2451,2454,2457,2460],{"className":2447},[619],[573,2449],{"className":2450,"style":2383},[623],[573,2452,1173],{"className":2453},[628],[573,2455],{"className":2456,"style":1049},[756],[573,2458,893],{"className":2459},[1053],[573,2461],{"className":2462,"style":1049},[756],[573,2464,2466,2469,2472,2475,2478],{"className":2465},[619],[573,2467],{"className":2468,"style":1895},[623],[573,2470,1173],{"className":2471},[628],[573,2473],{"className":2474,"style":1049},[756],[573,2476,2303],{"className":2477},[1053],[573,2479],{"className":2480,"style":1049},[756],[573,2482,2484,2487,2490,2493,2496,2499],{"className":2483},[619],[573,2485],{"className":2486,"style":624},[623],[573,2488,850],{"className":2489},[628],[573,2491,605],{"className":2492},[641],[573,2494],{"className":2495,"style":757},[756],[573,2497,666],{"className":2498},[761],[573,2500],{"className":2501,"style":757},[756],[573,2503,2505,2508,2511,2514,2517,2520,2523,2526,2529],{"className":2504},[619],[573,2506],{"className":2507,"style":624},[623],[573,2509,599],{"className":2510},[634],[573,2512,865],{"className":2513},[628],[573,2515,1173],{"className":2516},[628],[573,2518,674],{"className":2519},[780],[573,2521,678],{"className":2522},[756],[573,2524],{"className":2525,"style":787},[756],[573,2527,1718],{"className":2528},[628],[573,2530,605],{"className":2531},[641],[564,2533,2534,2535,2599,2600,2189,2830,2996],{},"Derselbe Vektor um ",[573,2536,2538,2557],{"className":2537},[576],[573,2539,2541],{"className":2540},[580],[582,2542,2543],{"xmlns":584},[586,2544,2545,2554],{},[589,2546,2547],{},[1708,2548,2549,2552],{},[1171,2550,2551],{},"30",[596,2553,2047],{},[607,2555,2556],{"encoding":609},"30^\\circ",[573,2558,2560],{"className":2559,"ariaHidden":615},[614],[573,2561,2563,2566,2570],{"className":2562},[619],[573,2564],{"className":2565,"style":2060},[623],[573,2567,2569],{"className":2568},[628],"3",[573,2571,2573,2576],{"className":2572},[628],[573,2574,850],{"className":2575},[628],[573,2577,2579],{"className":2578},[1794],[573,2580,2582],{"className":2581},[704],[573,2583,2585],{"className":2584},[708],[573,2586,2588],{"className":2587,"style":2060},[712],[573,2589,2590,2593],{"style":1807},[573,2591],{"className":2592,"style":1811},[719],[573,2594,2596],{"className":2595},[1815,1816,999,1817],[573,2597,2047],{"className":2598},[1053,1817],": Mit ",[573,2601,2603,2637],{"className":2602},[576],[573,2604,2606],{"className":2605},[580],[582,2607,2608],{"xmlns":584},[586,2609,2610,2634],{},[589,2611,2612,2614,2616,2622,2624],{},[592,2613,857],{},[596,2615,860],{},[1708,2617,2618,2620],{},[1171,2619,2551],{},[596,2621,2047],{},[596,2623,666],{},[2625,2626,2627,2632],"mfrac",{},[2628,2629,2630],"msqrt",{},[1171,2631,2569],{},[1171,2633,1718],{},[607,2635,2636],{"encoding":609},"\\cos 30^\\circ = \\frac{\\sqrt3}{2}",[573,2638,2640,2693],{"className":2639,"ariaHidden":615},[614],[573,2641,2643,2646,2649,2652,2655,2684,2687,2690],{"className":2642},[619],[573,2644],{"className":2645,"style":2060},[623],[573,2647,857],{"className":2648},[1039],[573,2650],{"className":2651,"style":787},[756],[573,2653,2569],{"className":2654},[628],[573,2656,2658,2661],{"className":2657},[628],[573,2659,850],{"className":2660},[628],[573,2662,2664],{"className":2663},[1794],[573,2665,2667],{"className":2666},[704],[573,2668,2670],{"className":2669},[708],[573,2671,2673],{"className":2672,"style":2060},[712],[573,2674,2675,2678],{"style":1807},[573,2676],{"className":2677,"style":1811},[719],[573,2679,2681],{"className":2680},[1815,1816,999,1817],[573,2682,2047],{"className":2683},[1053,1817],[573,2685],{"className":2686,"style":757},[756],[573,2688,666],{"className":2689},[761],[573,2691],{"className":2692,"style":757},[756],[573,2694,2696,2700],{"className":2695},[619],[573,2697],{"className":2698,"style":2699},[623],"height:1.383em;vertical-align:-0.345em;",[573,2701,2703,2707,2827],{"className":2702},[628],[573,2704],{"className":2705},[634,2706],"nulldelimiter",[573,2708,2710],{"className":2709},[2625],[573,2711,2713,2818],{"className":2712},[704,1013],[573,2714,2716,2815],{"className":2715},[708],[573,2717,2720,2735,2746],{"className":2718,"style":2719},[712],"height:1.038em;",[573,2721,2723,2726],{"style":2722},"top:-2.655em;",[573,2724],{"className":2725,"style":720},[719],[573,2727,2729],{"className":2728},[1815,1816,999,1817],[573,2730,2732],{"className":2731},[628,1817],[573,2733,1718],{"className":2734},[628,1817],[573,2736,2738,2741],{"style":2737},"top:-3.23em;",[573,2739],{"className":2740,"style":720},[719],[573,2742],{"className":2743,"style":2745},[2744],"frac-line","border-bottom-width:0.04em;",[573,2747,2749,2752],{"style":2748},"top:-3.399em;",[573,2750],{"className":2751,"style":720},[719],[573,2753,2755],{"className":2754},[1815,1816,999,1817],[573,2756,2758],{"className":2757},[628,1817],[573,2759,2762],{"className":2760},[628,2761,1817],"sqrt",[573,2763,2765,2806],{"className":2764},[704,1013],[573,2766,2768,2803],{"className":2767},[708],[573,2769,2772,2783],{"className":2770,"style":2771},[712],"height:0.9128em;",[573,2773,2776,2779],{"className":2774,"style":715},[2775],"svg-align",[573,2777],{"className":2778,"style":720},[719],[573,2780,2569],{"className":2781,"style":2782},[628,1817],"padding-left:0.833em;",[573,2784,2786,2789],{"style":2785},"top:-2.8728em;",[573,2787],{"className":2788,"style":720},[719],[573,2790,2794],{"className":2791,"style":2793},[2792,1817],"hide-tail","min-width:0.853em;height:1.08em;",[741,2795,2800],{"xmlns":743,"width":2796,"height":2797,"viewBox":2798,"preserveAspectRatio":2799},"400em","1.08em","0 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1{,}87).",[573,3072,3074,3360,3391],{"className":3073,"ariaHidden":615},[614],[573,3075,3077,3081,3351,3354,3357],{"className":3076},[619],[573,3078],{"className":3079,"style":3080},[623],"height:1.8em;vertical-align:-0.65em;",[573,3082,3084,3091,3138,3141,3144,3147,3215,3218,3221,3224,3227,3230,3233,3236,3345],{"className":3083},[989],[573,3085,3087],{"className":3086,"style":994},[634,993],[573,3088,599],{"className":3089},[998,3090],"size2",[573,3092,3094],{"className":3093},[628,2761],[573,3095,3097,3129],{"className":3096},[704,1013],[573,3098,3100,3126],{"className":3099},[708],[573,3101,3104,3113],{"className":3102,"style":3103},[712],"height:0.9561em;",[573,3105,3107,3110],{"className":3106,"style":715},[2775],[573,3108],{"className":3109,"style":720},[719],[573,3111,2569],{"className":3112,"style":2782},[628],[573,3114,3116,3119],{"style":3115},"top:-2.9161em;",[573,3117],{"className":3118,"style":720},[719],[573,3120,3122],{"className":3121,"style":2793},[2792],[741,3123,3124],{"xmlns":743,"width":2796,"height":2797,"viewBox":2798,"preserveAspectRatio":2799},[750,3125],{"d":2802},[573,3127,1124],{"className":3128},[1123],[573,3130,3132],{"className":3131},[708],[573,3133,3136],{"className":3134,"style":3135},[712],"height:0.0839em;",[573,3137],{},[573,3139],{"className":3140,"style":1049},[756],[573,3142,865],{"className":3143},[1053],[573,3145],{"className":3146,"style":1049},[756],[573,3148,3150,3153,3212],{"className":3149},[628],[573,3151],{"className":3152},[634,2706],[573,3154,3156],{"className":3155},[2625],[573,3157,3159,3204],{"className":3158},[704,1013],[573,3160,3162,3201],{"className":3161},[708],[573,3163,3165,3179,3187],{"className":3164,"style":2944},[712],[573,3166,3167,3170],{"style":2722},[573,3168],{"className":3169,"style":720},[719],[573,3171,3173],{"className":3172},[1815,1816,999,1817],[573,3174,3176],{"className":3175},[628,1817],[573,3177,1718],{"className":3178},[628,1817],[573,3180,3181,3184],{"style":2737},[573,3182],{"className":3183,"style":720},[719],[573,3185],{"className":3186,"style":2745},[2744],[573,3188,3189,3192],{"style":2969},[573,3190],{"className":3191,"style":720},[719],[573,3193,3195],{"className":3194},[1815,1816,999,1817],[573,3196,3198],{"className":3197},[628,1817],[573,3199,1173],{"className":3200},[628,1817],[573,3202,1124],{"className":3203},[1123],[573,3205,3207],{"className":3206},[708],[573,3208,3210],{"className":3209,"style":2824},[712],[573,3211],{},[573,3213],{"className":3214},[641,2706],[573,3216,674],{"className":3217},[780],[573,3219,678],{"className":3220},[756],[573,3222],{"className":3223,"style":787},[756],[573,3225,1173],{"className":3226},[628],[573,3228],{"className":3229,"style":1049},[756],[573,3231,893],{"className":3232},[1053],[573,3234],{"className":3235,"style":1049},[756],[573,3237,3239,3242,3342],{"className":3238},[628],[573,3240],{"className":3241},[634,2706],[573,3243,3245],{"className":3244},[2625],[573,3246,3248,3334],{"className":3247},[704,1013],[573,3249,3251,3331],{"className":3250},[708],[573,3252,3254,3268,3276],{"className":3253,"style":2719},[712],[573,3255,3256,3259],{"style":2722},[573,3257],{"className":3258,"style":720},[719],[573,3260,3262],{"className":3261},[1815,1816,999,1817],[573,3263,3265],{"className":3264},[628,1817],[573,3266,1718],{"className":3267},[628,1817],[573,3269,3270,3273],{"style":2737},[573,3271],{"className":3272,"style":720},[719],[573,3274],{"className":3275,"style":2745},[2744],[573,3277,3278,3281],{"style":2748},[573,3279],{"className":3280,"style":720},[719],[573,3282,3284],{"className":3283},[1815,1816,999,1817],[573,3285,3287],{"className":3286},[628,1817],[573,3288,3290],{"className":3289},[628,2761,1817],[573,3291,3293,3323],{"className":3292},[704,1013],[573,3294,3296,3320],{"className":3295},[708],[573,3297,3299,3308],{"className":3298,"style":2771},[712],[573,3300,3302,3305],{"className":3301,"style":715},[2775],[573,3303],{"className":3304,"style":720},[719],[573,3306,2569],{"className":3307,"style":2782},[628,1817],[573,3309,3310,3313],{"style":2785},[573,3311],{"className":3312,"style":720},[719],[573,3314,3316],{"className":3315,"style":2793},[2792,1817],[741,3317,3318],{"xmlns":743,"width":2796,"height":2797,"viewBox":2798,"preserveAspectRatio":2799},[750,3319],{"d":2802},[573,3321,1124],{"className":3322},[1123],[573,3324,3326],{"className":3325},[708],[573,3327,3329],{"className":3328,"style":2812},[712],[573,3330],{},[573,3332,1124],{"className":3333},[1123],[573,3335,3337],{"className":3336},[708],[573,3338,3340],{"className":3339,"style":2824},[712],[573,3341],{},[573,3343],{"className":3344},[641,2706],[573,3346,3348],{"className":3347,"style":994},[641,993],[573,3349,605],{"className":3350},[998,3090],[573,3352],{"className":3353,"style":757},[756],[573,3355,3052],{"className":3356},[761],[573,3358],{"className":3359,"style":757},[756],[573,3361,3363,3366,3369,3372,3378,3382,3385,3388],{"className":3362},[619],[573,3364],{"className":3365,"style":624},[623],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Drehung von ",[573,3420,3422,3446],{"className":3421},[576],[573,3423,3425],{"className":3424},[580],[582,3426,3427],{"xmlns":584},[586,3428,3429,3443],{},[589,3430,3431,3433,3435,3437,3439,3441],{},[596,3432,599],{"stretchy":598},[1171,3434,2569],{},[596,3436,674],{"separator":615},[676,3438,678],{},[1171,3440,850],{},[596,3442,605],{"stretchy":598},[607,3444,3445],{"encoding":609},"(3,\\ 0)",[573,3447,3449],{"className":3448,"ariaHidden":615},[614],[573,3450,3452,3455,3458,3461,3464,3467,3470,3473],{"className":3451},[619],[573,3453],{"className":3454,"style":624},[623],[573,3456,599],{"className":3457},[634],[573,3459,2569],{"className":3460},[628],[573,3462,674],{"className":3463},[780],[573,3465,678],{"className":3466},[756],[573,3468],{"className":3469,"style":787},[756],[573,3471,850],{"className":3472},[628],[573,3474,605],{"className":3475},[641]," um ",[573,3478,3480,3500],{"className":3479},[576],[573,3481,3483],{"className":3482},[580],[582,3484,3485],{"xmlns":584},[586,3486,3487,3497],{},[589,3488,3489,3491],{},[596,3490,865],{},[1708,3492,3493,3495],{},[1171,3494,2044],{},[596,3496,2047],{},[607,3498,3499],{"encoding":609},"-90^\\circ",[573,3501,3503],{"className":3502,"ariaHidden":615},[614],[573,3504,3506,3510,3513,3516],{"className":3505},[619],[573,3507],{"className":3508,"style":3509},[623],"height:0.7574em;vertical-align:-0.0833em;",[573,3511,865],{"className":3512},[628],[573,3514,2064],{"className":3515},[628],[573,3517,3519,3522],{"className":3518},[628],[573,3520,850],{"className":3521},[628],[573,3523,3525],{"className":3524},[1794],[573,3526,3528],{"className":3527},[704],[573,3529,3531],{"className":3530},[708],[573,3532,3534],{"className":3533,"style":2060},[712],[573,3535,3536,3539],{"style":1807},[573,3537],{"className":3538,"style":1811},[719],[573,3540,3542],{"className":3541},[1815,1816,999,1817],[573,3543,2047],{"className":3544},[1053,1817]," (im Uhrzeigersinn) ergibt ",[573,3547,3549,3575],{"className":3548},[576],[573,3550,3552],{"className":3551},[580],[582,3553,3554],{"xmlns":584},[586,3555,3556,3572],{},[589,3557,3558,3560,3562,3564,3566,3568,3570],{},[596,3559,599],{"stretchy":598},[1171,3561,850],{},[596,3563,674],{"separator":615},[676,3565,678],{},[596,3567,865],{},[1171,3569,2569],{},[596,3571,605],{"stretchy":598},[607,3573,3574],{"encoding":609},"(0,\\ 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Dann dreht man im Uhrzeigersinn statt dagegen. Kontrolle: ",[573,3618,3620,3643],{"className":3619},[576],[573,3621,3623],{"className":3622},[580],[582,3624,3625],{"xmlns":584},[586,3626,3627,3641],{},[589,3628,3629,3631,3633,3635,3637,3639],{},[596,3630,599],{"stretchy":598},[1171,3632,1173],{},[596,3634,674],{"separator":615},[676,3636,678],{},[1171,3638,850],{},[596,3640,605],{"stretchy":598},[607,3642,1184],{"encoding":609},[573,3644,3646],{"className":3645,"ariaHidden":615},[614],[573,3647,3649,3652,3655,3658,3661,3664,3667,3670],{"className":3648},[619],[573,3650],{"className":3651,"style":624},[623],[573,3653,599],{"className":3654},[634],[573,3656,1173],{"className":3657},[628],[573,3659,674],{"className":3660},[780],[573,3662,678],{"className":3663},[756],[573,3665],{"className":3666,"style":787},[756],[573,3668,850],{"className":3669},[628],[573,3671,605],{"className":3672},[641]," muss bei kleinem positivem Winkel nach oben wandern.",[1444,3675,3676],{},"Den Taschenrechner im Bogenmaß lassen, obwohl der Winkel in Grad 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drehen, ohne vorher zu verschieben.",{"title":3775,"searchDepth":3776,"depth":3776,"links":3777},"",2,[3778,3779,3780],{"id":561,"depth":3776,"text":562},{"id":1965,"depth":3776,"text":1966},{"id":3610,"depth":3776,"text":3611},[3782,3785,3788,3791,3794,3796,3799,3802,3805,3808,3810],{"lhs":3783,"rhs":3784},"multiply([[cos(x), -sin(x)], [sin(x), cos(x)]], [[cos(y), -sin(y)], [sin(y), cos(y)]])[1, 1]","cos(x + y)",{"lhs":3786,"rhs":3787},"multiply([[cos(x), -sin(x)], [sin(x), cos(x)]], [[cos(y), -sin(y)], [sin(y), cos(y)]])[2, 1]","sin(x + y)",{"lhs":3789,"rhs":3790},"(p*cos(x) - q*sin(x))^2 + (p*sin(x) + q*cos(x))^2","p^2 + q^2",{"lhs":3792,"rhs":3793},"2*cos(90*pi\u002F180) - 1*sin(90*pi\u002F180)","-1",{"lhs":3795,"rhs":1718},"2*sin(90*pi\u002F180) + 1*cos(90*pi\u002F180)",{"lhs":3797,"rhs":3798},"2*cos(30*pi\u002F180) - 1*sin(30*pi\u002F180)","sqrt(3) - 0.5",{"lhs":3800,"rhs":3801},"2*sin(30*pi\u002F180) + 1*cos(30*pi\u002F180)","1 + sqrt(3)\u002F2",{"lhs":3803,"rhs":3804},"round(sqrt(3) - 0.5, 2)","1.23",{"lhs":3806,"rhs":3807},"round(1 + sqrt(3)\u002F2, 2)","1.87",{"lhs":3809,"rhs":850},"3*cos(-90*pi\u002F180) - 0*sin(-90*pi\u002F180)",{"lhs":3811,"rhs":3812},"3*sin(-90*pi\u002F180) + 0*cos(-90*pi\u002F180)","-3",null,"md","rotation-matrix","R(\\varphi) = \\begin{pmatrix} \\cos\\varphi & -\\sin\\varphi \\\\ \\sin\\varphi & \\cos\\varphi \\end{pmatrix}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmtable rowspacing=\"0.16em\" columnalign=\"center center\" columnspacing=\"1em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>φ\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>φ\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>φ\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>φ\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R(\\varphi) = \\begin{pmatrix} \\cos\\varphi & -\\sin\\varphi \\\\ \\sin\\varphi & \\cos\\varphi \\end{pmatrix}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C\u002Fspan>\u003Cspan class=\"arraycolsep\" style=\"width:0.5em;\">\u003C\u002Fspan>\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.45em;\">\u003Cspan style=\"top:-3.61em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.41em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.95em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdrehmatrix",[],[3824,3825,3826,3827],"matrix-multiplication","orthogonal-matrix","unit-circle","angle-between-vectors",{"title":548,"description":3775},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdrehmatrix","Die Drehmatrix R(φ) dreht jeden Vektor der Ebene um den Winkel φ gegen den Uhrzeigersinn um den Ursprung.",[3832,3833,3834,3835,3836],"drehmatrix","drehung","rotation","matrix","abbildung",[3838,3841],{"symbol":610,"meaning":3839,"symbolHtml":3840},"Drehmatrix zum Drehwinkel φ","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R(\\varphi)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3842,"meaning":3843,"symbolHtml":3844},"\\varphi","Drehwinkel, positiv gegen den Uhrzeigersinn","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>φ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\varphi\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","AZnKgYuHUi0wJ8NZrd3KcUBuCbGSycgnd39ed4xTLus",[3847,3850,3853,3856],{"stem":3848,"title":3849,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fmatrizenmultiplikation","Matrizenmultiplikation",{"stem":3851,"title":3852,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Forthogonale-matrix","Orthogonale Matrix",{"stem":3854,"title":3855,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fwinkel-zwischen-zwei-vektoren","Winkel zwischen zwei Vektoren",{"stem":3857,"title":3858,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Feinheitskreis","Sinus und Kosinus am Einheitskreis",1793824277834]