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