${}_{xy}=-150$mPa

${}_x=-180$MPa

${}_y=0$MPa.

The state of stress at a pount is shown in element $A.$

Determine:

$($a$)$ the prinapal stresses, ${}_{1,2}$

$($b$)$ the maximum in$-$plane shear stress, ${}_{\text{m}\text{a}\text{x}}$ in$-$plane.

$($c$)$ Average stress.

$($d$)$ The orientation principal stress.

$($e$)$ The ${}_x^{\text{'}},{}_y^{\text{'}}$ and ${}_{xy}^{\text{'}}$