评分及理由

（1）得分及理由（满分4分）

学生作答为：{0,1,y-1}，与标准答案\(\{0,1, y-1\}\)完全一致。旋度计算公式为： \[ \text{rot}\boldsymbol{A} = \left( \frac{\partial Q}{\partial y} - \frac{\partial P}{\partial z}, \frac{\partial P}{\partial x} - \frac{\partial R}{\partial y}, \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right) \] 其中\(\boldsymbol{A} = (P, Q, R) = (x+y+z, xy, z)\)。计算可得： - 第一分量：\(\frac{\partial Q}{\partial y} - \frac{\partial P}{\partial z} = x - 1\)？等等，重新计算： \(\frac{\partial Q}{\partial y} = \frac{\partial (xy)}{\partial y} = x\)，\(\frac{\partial P}{\partial z} = \frac{\partial (x+y+z)}{\partial z} = 1\)，所以第一分量为\(x - 1\)？但标准答案是0。这里需要仔细核对： 实际上旋度公式为： \[ \nabla \times \boldsymbol{A} = \begin{vmatrix} \boldsymbol{i} & \boldsymbol{j} & \boldsymbol{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ P & Q & R \end{vmatrix} \] 展开后： - \(\boldsymbol{i}\)分量：\(\frac{\partial R}{\partial y} - \frac{\partial...