Please provide work $/$ rationale for each part to be eligible for full credit.

Consider a geometric zero frame fixed in space. If an object begins at the origin of this zero frame $,$ and in alignment with its axes, please consider the the transformation described below which brings the object to the one frame.

$-$ A translation of $-3$ units along the fixed $\backslash ($ x $\backslash )-$axis, followed by

$-$ a rotation of $\backslash (-\backslash$frac$\{\backslash$pi$\}\{2\}\backslash$mathrm$\{$rad$\}\backslash )$ about the fixed $\backslash ($ z $\backslash )-$axis, followed by

$-$ a rotation of $\backslash (\backslash$frac$\{\backslash$pi$\}\{2\}\backslash$mathrm$\{$rad$\}\backslash )$ about the current z $-$axis.

All results should include numeric values.

$1.(6$ pts$)$ Compute the homogenous transform $\backslash ($ T$\_\{1\}^\{0\}\backslash )$ that describes the one frame as perceived from the zero frame.

$2.(1$ pts$)$ What are the coordinates of the one frame's origin with respect to the zero frame's origin?

$3.(1$ pts$)$ What is the $\backslash (3$ x $3\backslash )$ rotation matrix relating the orientation of the one frame to the zero frame?

$4.(2$ pts$)$ What is the homogenous transformation describing the zero frame as perceived from the one frame?