L$-2.$ Point A is located on a Vexcel Imaging UltraCam Eagle Mark $3$ digital image whose orthogonal angular orientation matrix taking the object space $xYZ$ coordinate system to the image space xyz coordinate system is shown below. The camera used to photograph point A has a $100\mathrm{.}5$ mm focal length lens and the principal point offset is $(x_0=0,x_0=-0\mathrm{.}080)mm.$ The exposure station coordinates of the image are $x_L=10,000ft,Y_L=10,000,$ and the flying height above mean sea level is $3895\mathrm{.}48$ ft$.$ The image space coordinates for point A imaged on the photograph are$({}_s=-15\mathrm{.}996mm,y_s=-18\mathrm{.}320).$ Point A has an elevation of $842\mathrm{.}63$ feet above mean seal level.

Provide answers to the nearest integer for unitless answers and to $3$ placeholders to the right of the decimal point $(0\mathrm{.}000)$ for angular values $($in degrees$).$

$M=\left[\begin{array}{ccc}\sqrt[\phantom{2}]{0\mathrm{.}5}& \sqrt[\phantom{2}]{0\mathrm{.}5}& 0\\ -\sqrt[\phantom{2}]{0\mathrm{.}5}& \sqrt[\phantom{2}]{0\mathrm{.}5}& 0\\ 0& 0& 1\end{array}\right]$

a$)$ What is the value of the sum of the squared row $2$ elements $(m_{21},m_{22},m_{23})?$

b$)$ What is the angle the object space $x$ axis makes with the image space $y$ axis?

c$)$ What is the yaw $($kappa$)$ angle in the roll$-$pitch$-$yaw orientation system?

d$)$ What are the object space coordinates $(x_A,Y_A)$ for point A $($to $0\mathrm{.}01$ ft$)?$