We want to translate and rotate the 2D point \( \mathbf{p} = [2\ \ 0]^\top \)
The translation vector is \( [-2\ \ 0]^\top \).
The rotation is by \( 90^\circ \). What are the approximate coordinates of the point after the transform?
✱Translation followed by rotation:
✱Rotation followed by translation:
✱Does the order in which the rotation and translation are applied matter?
The matrix \( \mathbf{M_2} \) rotates a 2D point by 45 degrees.
$$
\mathbf{M_2} = \left[
\begin{array}{cc}
\cos{45^\circ} & -\sin{45^\circ} \\
\sin{45^\circ} & \cos{45^\circ} \\
\end{array}
\right]
$$
✱What is the rotation that will rotate a 3D point by 45 degrees around the z-axis?