Q$.3(30$ points$)$ A stress element is shown in Fig.Q$3.$

$($a$).$ Draw the Mohr's circle.

$($b$).$ Determine the principal planes and the principal stresses.

$($c$).$ Draw the stress element based on the principal coordinates. That is$,$ show the results obtained in Q$\mathrm{.}3($b$)$ on a sketch of a properly oriented element.

$($d$).$ Given $\backslash (\backslash$theta$=15^\{\backslash$circ$\}\backslash )$ counterclockwise, find $\backslash (\backslash$sigma$\_\{$y$\}^\{\backslash$prime$\}\backslash )$ based on the transformation equation.