化简下列方程[p=align:center][tex=12.214x1.429]cYzq4uSQ5djwLDa1cYNuQpVv7rRIopOF2+3ecG74IerjfIsPmdsqG/GqYVK0BXph[/tex].

2022-06-06

化简下列方程[p=align:center][tex=12.214x1.429]cYzq4uSQ5djwLDa1cYNuQpVv7rRIopOF2+3ecG74IerjfIsPmdsqG/GqYVK0BXph[/tex].

答案：

第一步，进行旋转变换，旋转角[tex=0.5x1.0]qm+hGi0qngLh1B7HsENMPg==[/tex]适合[p=align:center][tex=11.929x2.5]IYZooW4v0LijfCSnuWZN+CIfiEzaqnFYTYMxdim79xyYmCpL/iyM+9cgAa5geWRl3QH3vsI9rbankavV6KHXWDRCGLLgcyHNaS/vvkvBN9k=[/tex]，可取[tex=5.143x2.357]gHy9mFUt+2R+09nhV7SsUXlK8+OreWa1AMxiuGd+d9U=[/tex]，从而有[tex=4.5x2.643]ygfZlvzwlafYYdOD9WDuZ7iQJUjtVbOL+1jFh3HGnfI1JVS/KEQcmxxQBriL/Cf4[/tex]，[tex=4.571x2.643]sncjrn5F3GcBa5X5h7rpDyIGPpnPwL+EanMw3LSZbRE7xUeZLdbWA5NMwPPb1l/Z[/tex].由旋转变换公式, 有[p=align:center][tex=9.5x5.786]7EJHVCtO2IWq3KpdB+jQsq9JVZH54ShvX7XyzAzMSeNW62avTL5nK9Tnnr1TRFYnNjnGb7gYDCxAgv1hLuIf83fgNpjrpsv5xdz/C5BdSHdnmmGdxtjvSY8z6yD7PAbELyMmoVUaTwxyCqKyTdNBNXm74RwaDu/X98DQ1yrnLn/POFbWrpJFh+LLcOQIBVPCXT3xA8yTbQIQPyj2Xlaqv1atRSYCgkQDh1xv2O+YLdU=[/tex]，代入已知方程，化简得[p=align:right][tex=10.071x1.5]5eW3J4QBaqKIV4UnBLUPKqc5urJhJALeBHrZDqN506iLb9mSwE4E8BIhc5FRIgvvzuS+Z5OSyoQD2XQcXMniRw==[/tex].                             （1）第二步，进行平移变换.将（1）配方化为[p=align:center][tex=10.357x2.357]iyG/7oa2vj7fWvb5/yd8MF1MWY8FQ2iio6Yj6/U4V40clg8cf2CuP/o6jOFeNQPr5gOYpjTTb19q8qbQHz83Ow==[/tex]，作平移[p=align:center][tex=6.571x3.357]7EJHVCtO2IWq3KpdB+jQsrB6api6XTiW4A20y5aW7YwOvqkkIAkJoxRWPQK0LBMRZDcMn/TDeswsYO0jNz9Htx9yWc3ZMEaX+nUdrvx0GcF5UBf3xov3df458er6hFsTVigHKyb0Xwt2QhF07Ijd3Li6M1DJzJx8Yebx3O3xcJ4=[/tex]，得[p=align:center][tex=7.0x1.429]ZMJsl8t1YYCHdXNmG4IBy0hvLVfkpXMNRYVdXvugEhjyvARrKEHaqYMqsbwbdLAObkfxjaDjeNzGVLINEl2yvA==[/tex].

举一反三

内容

0
用 [tex=0.714x1.0]RRR4SYyCqv01G5bWEEMPdw==[/tex] 变换法解下列差分方程:[tex=19.214x1.357]p6lLLi8JdFlgAhKX3MZJGikBDmXhPuJpvkPy0b6xJnQBpn4obECtm9bJaCLvQmdPWK9xgXMede3BbizckbyU3A==[/tex][p=align:center]
1
证明设[tex=2.929x1.357]f8vXhXZkntbtcn5YtNszyA==[/tex]为循环群. （1）如果[tex=3.143x1.357]+ffGqEoCaO1XtD5rcTB2lg==[/tex],则[tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex]的全部子群为[p=align:center][tex=10.0x1.571]ASO79Lx7XorIzXfD+OkCX2aw3jZQI9gX9hIKxPpEoHVfIf8jaMNsVAI3GKreTubJeTAOApOyglKnt7BLTl+WYZ4hCtb/6NuRQOp+iQCSiHw=[/tex].（2）如果[tex=3.0x1.357]o/dVgihcop3NMKmdwvgkeQ==[/tex]则[tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex]的全部子群为[p=align:center][tex=3.857x1.571]ho2B7oQoeaJgTzqz5bQYfbOIXX6Nns7PiwvcUM/c6htf+U69GXScKgmyziwSNCkFVSjjsPHGOR5r/3zKWR4nMg==[/tex] 为[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 的正因子 .[p=align:center][br][/br][p=align:center]
2
用不变量判别下列方程表示何种曲线.[p=align:center][tex=9.429x1.429]jLrRVyqmdoMx67C7lZ+MPKD/FjrxDl67AK1KAsj7kTU=[/tex].
3
设矩阵[p=align:center][tex=22.143x3.643]+HNIZcMaSzNwCe0LO7bsUq/nNqiD9uPVTX2/0HTi4M1ZunAEz7qfA0Rd4ovBDZfbF0GGptIGukHKOpbU4T80nTzErVwKYTs47PXy7I1XE++qtUmsh208vGDr7MXpYVMuue4tfvhHRJLpbtyk1c9gflSH5Tkz0UMsPjui7wPzKBU08/vB+N4sKYnD/Q0clHeQK7pT2y7o9KK3BmOLD7xVrZgRj2iFXMh2GeWPZ6MQh2cc/+VI9kCbffCxY/5NFhhEg5peWRqbWgbcZiOGAvr4nJHWN3qjueDxOqTvbDaTM3I=[/tex](1) 求 [tex=3.357x1.214]03ql8P+0CvRd0jLgTuf2VbT/wkB2igrddY7J5Strl0NU0hh6vIeN8jScC63B9GnL[/tex](2) 解矩阵方程 [tex=5.0x1.214]zvhQGTB3bj6p1+G/NgyQR3d8RUTq+KWJyJoscsNb5yO4fheydfGUyOSeXl9e1m/p[/tex] 求 [tex=1.286x1.214]J9ANNFCyxpObx83w0Vdt38yleCTlTu8vvnAXkiBZ7K0=[/tex]（3）解矩阵方程 [tex=11.786x1.357]hbnRNbrpLcfkctuGfn+sleqQROrTrwqqWds6OPLk7Wdn4vtQb1+Muj1i2/7A1FkoB4neXMMMBk0saIAf9uWaRm+qUEsJaMS5QeVJeBYZxhkTnaWiAitNyge3msYgxeJV[/tex] 求 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex].
4
就下列初始条件及边界条件解弦振动方程[p=align:center][tex=22.5x2.429]2UW5dL8rE/xf3SOJQw+jGq2h0sCfdRd7kSPweoAI2CiTZjmsYn9YXBQC4oBuenzf1cZVucm0Q+2ok60584ltNcajAewBObWrG6vvOEx+dcNF9PgcRC7T7Cg1tOq6lfVA[/tex]