Transformations Between $3$D Coordinate Systems: Consider two $3$D coordinate systems:

System A has its origin at $(1,1,1)$ and is aligned with the world axes.

System B has its origin at $(2,2,2)$ and is rotated by $90$ around the Z $-$axis.

A point $r=(3,3,3)$ is given in System A$.$ Compute the transformation matrix to convert this

point to System B$\text{'}$s coordinates and apply it to $r.$