QUESION5 Local Rotation Choose one $\cdot 5$ points Write the local rotation matrix of 90 about the local Zaxis, ${ }^{B_{Z}}(90)$ \[ \left(\begin{array}{ccc} 0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right) \] \[ \left(\begin{array}{ccc} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right) \] \[ \left(\begin{array}{lll} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right) \]

Step 1 ：The problem is asking for the local rotation matrix of 90 degrees about the local Z-axis.

Step 2 ：The rotation matrix for a 90 degree rotation about the Z-axis is given by: \[\begin{bmatrix} cos(90) & -sin(90) & 0 \\ sin(90) & cos(90) & 0 \\ 0 & 0 & 1 \end{bmatrix}\]

Step 3 ：In this case, cos(90) = 0 and sin(90) = 1.

Step 4 ：So the rotation matrix becomes: \[\begin{bmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}\]

Step 5 ：Final Answer: The local rotation matrix of 90 degrees about the local Z-axis is \[\boxed{\begin{bmatrix} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}}\]