$4\mathrm{.}2)$ Consider the stress state given by $x=100$MPa,$y=150$MPa,$z=-50$MPa, and $xy=yz=zx=0$MPa. Determine the following:

$($a$)$ Principal normal stresses and principal shear stresses.

$($b$)$ Maximum normal stress and maximum shear stress.

$($c$)$ Show that, in this specific case where $xy=yz=zx=0,$ the principal normal stresses $1,2,3$ are equal to $x,y,z.$