题目03. 在\(\mathbb{R}^2\)中将向量逆时针旋转\(\theta\)角对应的旋转变换矩阵是：
A: \(\begin{pmatrix}\cos{\theta}& \sin{\theta}\\ \sin{\theta}& \cos{\theta}\end{pmatrix}\)
B: \(\begin{pmatrix}\cos{\theta}& -\sin{\theta}\\ \sin{\theta}& \cos{\theta}\end{pmatrix}\)
C: \(\begin{pmatrix}\cos{\theta}& \sin{\theta}\\ -\sin{\theta}& \cos{\theta}\end{pmatrix}\)
D: \(\begin{pmatrix}\cos{\theta}& -\sin{\theta}\\ -\sin{\theta}& \cos{\theta}\end{pmatrix}\)
A: \(\begin{pmatrix}\cos{\theta}& \sin{\theta}\\ \sin{\theta}& \cos{\theta}\end{pmatrix}\)
B: \(\begin{pmatrix}\cos{\theta}& -\sin{\theta}\\ \sin{\theta}& \cos{\theta}\end{pmatrix}\)
C: \(\begin{pmatrix}\cos{\theta}& \sin{\theta}\\ -\sin{\theta}& \cos{\theta}\end{pmatrix}\)
D: \(\begin{pmatrix}\cos{\theta}& -\sin{\theta}\\ -\sin{\theta}& \cos{\theta}\end{pmatrix}\)
举一反三
- 下面哪个矩阵不是\(2\)阶酉矩阵？ A: \(\begin{pmatrix}e^i\cos{\theta}&e^i\sin{\theta}\\-e^i\sin{\theta}&e^i\cos{\theta}\end{pmatrix}\) B: \(\begin{pmatrix}\cos{\theta}&\sin{\theta}\\-\sin{\theta}&\cos{\theta}\end{pmatrix}\) C: \(\begin{pmatrix}1&0\\0&1\end{pmatrix}\) D: \(\begin{pmatrix}e^i\cos{\theta}&e^i\sin{\theta}\\e^{-i}\sin{\theta}&e^i\cos{\theta}\end{pmatrix}\)
- 两个全同粒子，自旋为0，那么它们相互碰撞的微分散射截面的表达式为： A: $\sigma(\theta,\varphi)=|f(\theta,\varphi)-f(\pi-\theta,\pi-\varphi)|^2$ B: $\sigma(\theta,\varphi)=|f(\theta,\varphi)+f(\pi-\theta,\pi-\varphi)|^2$ C: $\sigma(\theta,\varphi)=|f(\theta,\varphi)+f(\pi-\theta,\pi+\varphi)|^2$ D: $\sigma(\theta,\varphi)=|f(\theta,\varphi)-f(\pi-\theta,\pi+\varphi)|^2$
- 下列哪个矩阵的列空间是和其他三个矩阵的列空间不同的 A: \(\begin{pmatrix} 1 & -1 & 1 \\ -1 & 1 & 1 \\ 1 & -1 & 1 \end{pmatrix}\) B: \(\begin{pmatrix} -1 & 1 \\ 1 & 1 \\ -1 & 1 \end{pmatrix}\) C: \(\begin{pmatrix} 1 & -1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & -1 \end{pmatrix}\) D: \(\begin{pmatrix} 2 & 0 & 2 \\ -2 & 1 & 2 \\ 2 & 0 & 2 \end{pmatrix}\)
- 随机矢量空间中，待估计量\(\theta \)在观测量\(z\)上的投影可以记为： A: （A）\(\frac{{E(\theta z)}}{{E({\theta ^2})}}z\) B: （B）\(\frac{{E(\theta z)}}{{E({\theta ^2})}}\theta \) C: （C）\(\frac{{E(\theta z)}}{{E(z_{}^2)}}z\) D: （D）\(\frac{{E(\theta z)}}{{E(z_{}^2)}}\theta \)
- 下面哪个个方阵满足存在正整数\(n\),使得它的\(n\)次方是零矩阵? A: \(\begin{pmatrix} 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix}\) B: \(\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}\) C: \(\begin{pmatrix} 1 & -1 \\ 0 & 1 \end{pmatrix}\)