在空间取定直角坐标系 [tex=3.143x1.0]11uB8u/aa5tBPn0lc/2zwg==[/tex] 以 [tex=0.857x1.0]JGak6BG8IqnzqFUlidM8wQ==[/tex] 表示空间绕 [tex=1.643x1.0]FE9IowmQhmFQWxnEPOl1+w==[/tex] 轴由 [tex=1.571x1.286]Egwgc/sA4c91SnJo8hcqpw==[/tex] 向 [tex=1.5x1.0]eSux/eDx7IGn9pvVEa9VoA==[/tex] 方向旋转 [tex=1.429x1.071]0x1sflXOqrsdrJlmAbVenQ==[/tex] 的变换，以 [tex=0.714x1.0]UF6bSrGL+IxoE78FFIRkgA==[/tex] 表示绕 [tex=1.571x1.286]Egwgc/sA4c91SnJo8hcqpw==[/tex] 轴由 [tex=1.5x1.0]eSux/eDx7IGn9pvVEa9VoA==[/tex] 向 [tex=1.643x1.0]FE9IowmQhmFQWxnEPOl1+w==[/tex] 方向旋转 [tex=1.429x1.071]0x1sflXOqrsdrJlmAbVenQ==[/tex] 的变换，以 [tex=0.571x1.0]SVbk6JgMC3iD8o/A9O6b0g==[/tex] 表示绕 [tex=1.5x1.0]eSux/eDx7IGn9pvVEa9VoA==[/tex] 轴由 [tex=1.643x1.0]FE9IowmQhmFQWxnEPOl1+w==[/tex] 向 [tex=1.571x1.286]Egwgc/sA4c91SnJo8hcqpw==[/tex] 方向旋转 [tex=1.429x1.071]0x1sflXOqrsdrJlmAbVenQ==[/tex] 的变换. 证明 [tex=6.357x1.214]QjLC2nJKcX7740JWxb7SVYVDV4INV7DTGrErQg0c9Ma96Z8p32Faa6Ui+JZoHELwg1mZeTXcoKOOnlq0i1wSRg==[/tex]；[tex=1.5x1.0]UZbiW+2K0+ZPZjkSkbzXng==[/tex][tex=0.786x1.286]94yQi4lF9xfg5bsYhw/rNQ==[/tex][tex=7.429x1.429]yZhMZrduGAuMEaMVc7GXey8T+zBFw+czE3vLGL9hZKIyErupBUbSMnuBYYYTsaI9JaDU1Cz/2m3NKRD3CBYcRZS/wKKCevjvGx8tchTEU+onNAJX4HcPCIWSLg5HyJix[/tex] 并验证 [tex=5.643x1.5]dh1Uq5ornjD+EDdKub98YzX2Ays3n5vOPyvvTaxwhnlrecsk0nlOusxVp4BTW0QjgzBL5bkwUrV9vJlYyW1MhA==[/tex] 是否成立.

2022-06-09

在空间取定直角坐标系 [tex=3.143x1.0]11uB8u/aa5tBPn0lc/2zwg==[/tex] 以 [tex=0.857x1.0]JGak6BG8IqnzqFUlidM8wQ==[/tex] 表示空间绕 [tex=1.643x1.0]FE9IowmQhmFQWxnEPOl1+w==[/tex] 轴由 [tex=1.571x1.286]Egwgc/sA4c91SnJo8hcqpw==[/tex] 向 [tex=1.5x1.0]eSux/eDx7IGn9pvVEa9VoA==[/tex] 方向旋转 [tex=1.429x1.071]0x1sflXOqrsdrJlmAbVenQ==[/tex] 的变换，以 [tex=0.714x1.0]UF6bSrGL+IxoE78FFIRkgA==[/tex] 表示绕 [tex=1.571x1.286]Egwgc/sA4c91SnJo8hcqpw==[/tex] 轴由 [tex=1.5x1.0]eSux/eDx7IGn9pvVEa9VoA==[/tex] 向 [tex=1.643x1.0]FE9IowmQhmFQWxnEPOl1+w==[/tex] 方向旋转 [tex=1.429x1.071]0x1sflXOqrsdrJlmAbVenQ==[/tex] 的变换，以 [tex=0.571x1.0]SVbk6JgMC3iD8o/A9O6b0g==[/tex] 表示绕 [tex=1.5x1.0]eSux/eDx7IGn9pvVEa9VoA==[/tex] 轴由 [tex=1.643x1.0]FE9IowmQhmFQWxnEPOl1+w==[/tex] 向 [tex=1.571x1.286]Egwgc/sA4c91SnJo8hcqpw==[/tex] 方向旋转 [tex=1.429x1.071]0x1sflXOqrsdrJlmAbVenQ==[/tex] 的变换. 证明 [tex=6.357x1.214]QjLC2nJKcX7740JWxb7SVYVDV4INV7DTGrErQg0c9Ma96Z8p32Faa6Ui+JZoHELwg1mZeTXcoKOOnlq0i1wSRg==[/tex]；[tex=1.5x1.0]UZbiW+2K0+ZPZjkSkbzXng==[/tex][tex=0.786x1.286]94yQi4lF9xfg5bsYhw/rNQ==[/tex][tex=7.429x1.429]yZhMZrduGAuMEaMVc7GXey8T+zBFw+czE3vLGL9hZKIyErupBUbSMnuBYYYTsaI9JaDU1Cz/2m3NKRD3CBYcRZS/wKKCevjvGx8tchTEU+onNAJX4HcPCIWSLg5HyJix[/tex] 并验证 [tex=5.643x1.5]dh1Uq5ornjD+EDdKub98YzX2Ays3n5vOPyvvTaxwhnlrecsk0nlOusxVp4BTW0QjgzBL5bkwUrV9vJlYyW1MhA==[/tex] 是否成立.

答案：

证  设 [tex=4.786x3.357]nLrbZ5Bnw/u3ymE11wBFagOOwBPbn32agKGJyAWddCj8ZbGAXwcGoJws5G7/LqnZ/v+UeES/z/iiUcRaUw3o8w==[/tex]，则[p=align:center][tex=6.214x3.357]5I+/Ll4sZHrlJyssDjpTsitqdu96Frh5GDAbC2jp+lHvfhgo7f90vSzGVVop0Ib8kbGOTgfTFgF0Sv2ouXRc8Wbm2HOVyWYh2NgytTMDFXE=[/tex]，[tex=6.643x3.5]VfJMl/JRDhUg4N/j0auYn/IqytUfpAtJTsAaBHGWbbpYtZUu4xe5RDX5kcc0Zy8+1t4EsVv8Adud00YOIzXb/yVY0Goc7HNoU5WF16p664aVi4r56DcGlH/Xq4DPjN+o[/tex]，[tex=5.929x3.357]QjLC2nJKcX7740JWxb7SVRsLpd50Ip1JM3oov8jA1nX4bSL7TkHJ8IDjjQellVI9mTCD3BQFa5cCiSh2G2vLbzyUeHc5B9WIe29CI0ZZPD8=[/tex]；[p=align:center][tex=6.214x3.357]jFUHvZdUMlNLdzJnP9l3ec1XERyJTJl8rQR5xyGwpYYmvF8c8w6hVsR6SG47yuf4xIcBfDX308D16+7fxqTOvH1DZQpeMOwKB4Dc9gHzDf8=[/tex]，[tex=6.571x3.5]C898K4q/O/zukGtPKnKKclM3AgVGqli7hg9rY2/WNtbE5Fhi96mQSQI36xd+JjWed8u1lZFzRXsgTu+V5zwNpWH50IjtJzcXM4c4FVROh09hN92Nni+QkaYQIw8bZ9Qn[/tex]，[tex=5.786x3.357]9i7Iv6uo1EnTx6/my6jqavm6zroy/yrwGP60pDHHUPomc/HBZSKC+BCUjAPqW8U1kyjW9s+TLfVXWA436tQa+0kk7D9MKRvHVfgdEIB228M=[/tex]；[p=align:center][tex=6.0x3.357]kXN7zCY+1A5RgGNsHKn4XKtrVg/QB5JIRw/bWoa1xtduPcUgWja2nvmpUkNG+ZPomtT+2LSc8ZiIo7JMmwxpIt2vvQ1WQxW/Xj9qQjLhFhQ=[/tex]，[tex=6.429x3.5]zhHln0/HETuqy490al1kATX0q54PO6Rv/RvSa5N9XecNAox2NSEUSUv6N2pa/Cw742KPIKARlPePAv/k6pWGH1qOzObyyPrB4rGIFvwITv+kxKWbXEDnMp6RFcJvnhL6[/tex]，[tex=5.714x3.357]IzV+mvkIcEK30KiKhrfMAQEug2BB7Y/1VWNsVvtBTDICu53CVJ2lcgjpbW9t54Qc6a4Jaq7uIxC2kIN/3Uz9Lt1UaaHZAjDFPQzW7db5Rpg=[/tex].于是 [tex=6.643x1.214]QjLC2nJKcX7740JWxb7SVYVDV4INV7DTGrErQg0c9Ma96Z8p32Faa6Ui+JZoHELwTdG7myTmSMBtxYSuqIIDhA==[/tex] 又[p=align:center][tex=6.214x3.357]I97gt1BhozBgAsZAP9goIOFCPKd88LWoxyBQXlhhQXuQeYuWTbeA/oICg0ln1nqa1ObUnn4m33nmtsrPrn5YIhdBWOO5fxcUAbPIWx7rtOg=[/tex]，[tex=7.0x3.5]u+8YQ5UZ8LFjP0K1k/8ZYGlQpyoldmV8VTEQFM5OjQoGYG06HtPqR/5gb7ff4dh7nXDTPKIcuqhrMPAtmlYjhMRIIYOckhPKIDI3Nn1m6JnUT6AH99adO9+Oe1O4ndK5[/tex]，故 [tex=1.5x1.0]OhMZlHwKHJ89mD+5c0gm9w==[/tex][tex=0.786x1.286]94yQi4lF9xfg5bsYhw/rNQ==[/tex][tex=1.5x1.0]9BAbVLXLjkRcOtappZwx+w==[/tex].又[p=align:center][tex=7.357x3.357]dh1Uq5ornjD+EDdKub98Y6iZ1sb+dyB17knEOvwpTZZ5ucGhKz/Q+/i1NYFXKkxh6XbT8Ng+cMqJoEZeqUaZ+A9JdexIjz0D4GAibz0+NFveINYuXl5CPdYa+KD8LRjH[/tex]，[tex=7.786x3.5]VfJMl/JRDhUg4N/j0auYn4rjo59VgIYYsbFY+kvXsOqcOeFSBs0FDGZt/L8V0C3RZDZ6GvGBwYcpv8ccCiX5UBcK9QI//G+m9lMYuW5DlibpW34fz3wN07acOXN9o3TscW5Cc1HKheKHZ+uooGm8+Q==[/tex]，故 [tex=2.643x1.5]dh1Uq5ornjD+EDdKub98YxdOb8YIHpznXr1zLqhCzBY=[/tex][tex=0.786x1.286]94yQi4lF9xfg5bsYhw/rNQ==[/tex][tex=2.286x1.214]Dq0CnAYXxSysEkEeuuNAZXM21+nPRZnkJoFWYAQWzhtnWQu+wG5SFJtCQu6yw+73[/tex].再注意到[p=align:center][tex=11.571x3.5]C898K4q/O/zukGtPKnKKcqvwIK6viNSpG4dxQ8l/MSA1J50wqzvPcIwUH7w3L1S8lrQWETiyfN24fy/YVQOHyLIQICZ92TcBVqAQIA0FKmOKLsZJzdG5e0trTnvoiDvqr3uxtZc6Vlf/YSvhbOVA5xoRw2DdsnRNGHnZHO0yG+V75A+jc06AlqUZQWOLxznN[/tex]，所以 [tex=5.286x1.214]C898K4q/O/zukGtPKnKKcqvwIK6viNSpG4dxQ8l/MSBw5INeJ0QCPhzcic9YS+CvpavgRXOpnYg/iUgIqOmpE9m/c42QNqBhdHFLgXv8Vnw=[/tex].

举一反三

内容

0
一物体沿x轴作简谐振动，振幅为[tex=2.357x1.0]7GPa9K44BRDikKhJCPFIzA==[/tex]，周期为[tex=1.0x1.0]HturbZDoPr8TFUP5kmSVXg==[/tex]，在[tex=1.643x1.0]xzdx0YYuEkZIVLSCfrKmTw==[/tex]时，[tex=3.214x1.0]GABhkK7XKY63I13Ox0uqtQ==[/tex]，且向x轴负方向运动，求运动方程。
1
由非空集合X的所有子集构成的集合称为X的幂集，记作[tex=1.143x1.214]6fgP1j+0v37iZFMJocAU+g==[/tex].（1）设X={a,b,c}，求[tex=1.143x1.214]6fgP1j+0v37iZFMJocAU+g==[/tex].（2）设X是由n个元素组成的有限集，证明[tex=1.143x1.214]6fgP1j+0v37iZFMJocAU+g==[/tex]中含有[tex=1.0x1.0]j//x0/Z+ltpf5R8ThFOpMA==[/tex]个元素.
2
设[tex=5.929x1.071]gAFI4ZzNAmjFfJAphmTsRQ==[/tex]，若[tex=7.786x1.357]09fTpcwFMVcu1qrv9hyVbjaVP6Nu0Q7b0o9JCaEhfzk=[/tex]，[tex=7.786x1.357]17Fg+KbtgLZdNaerla1J+g==[/tex]，[tex=7.714x1.357]GzWWzGNDry0+/hdju2Gv5Q==[/tex]，那么[tex=0.571x0.786]/uIIzJZ/1DPgc5sOsRpAXQ==[/tex]，[tex=0.571x1.0]Tr41q2//n6lfFMLRmh8s0w==[/tex]，[tex=0.5x0.786]rGd4FFr4Zsu+cuz6gxITMA==[/tex]的大小关系为 A: x<y<Z B: y<z<x C: z<x<y D: z<y<x E: 不能确定
3
>>>x= [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9]>>>print(x.sort()) 语句运行结果正确的是( )。 A: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] B: [10, 6, 0, 1, 7, 4, 3, 2, 8, 5, 9] C: [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0] D: ['2', '4', '0', '6', '10', '7', '8', '3', '9', '1', '5']
4
若:(1)函数 f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数;(2)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]有导数;(3)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数及函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数,则函数[tex=5.643x1.357]GmtX7Vop79exGU/rpqXUYw==[/tex]在已知点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]的可微性怎样?