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Transform exercise

1. 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?
   1. ✱Translation followed by rotation:
      
   2. ✱Rotation followed by translation:
      
2. ✱Does the order in which the rotation and translation are applied matter?
   
3. 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?