Problem $9$: A rigid body $B$ has its local reference frame $O_B{x}_B{y}_B{z}_B$ attached to the body and initially identical to the global frame Oxyz as shown in the figure below.

$($a$)$ Determine the rotation matrix of the body frame $O_B{x}_B{y}_B{z}_B$ with respect to the global frame Oxyz after performing the following consecutive rotation: rotate about $Oz$ axis by $90$ and followed by a rotation about the global $Oy$ axis by $90.$

$($b$)$ Point A$,$ B$,$ C$,$ D$,$ E and F are positioned by their coordinates with respect to the body frame $O_B{x}_B{y}_B{z}_B$ as shown in the figure. Determine the coordinate of each point with respect to the global frame Oxyz after performing the rotation in part $($a$)$

$($c$)$ Draw the new position of the rigid body after performing the above rotation.