For the given stress state, determine

$($a$)$ the principal stresses

$($b$)$ the orientation of the principal plane in degrees

$($c$)$ the maximum in$-$plane shear stress and associated average normal stress

$($d$)$ the orientation of the plane of maximum in$-$plane shear stress in degrees

$6_x=125mp{a}^{\sqrt[\phantom{2}]{?}+1}$

$6_y=-75$Mpa

${}_{xy}=50$Mpa$-1$