Problem $8$: Given $A,B$ and $C$ are three reference frames that have the following relationships: ${?}^A{R}^B=Z(-45)$ and ${?}^B{R}^C=x(-90).$

$($a$).$ Sketch the three reference frames.

$($b$).$ Find the rotation matrix ${?}^A{R}^C$ representing the orientation of frame $C$ with respect to frame $A.$

$($c$).$ A point M is positioned by its coordinates with respect to frame $C$ by $p_M^C=[2,-1,3{]}^T.$ Find its coordinates with respect to frame $A.$