$2-$ A brittle material has the properties $S_{ut}=30k$ and $S_{uc}=90k.$ Using the brittle Coulomb$-$Mohr theory, determine the factor of safety for the following states of plane stress.

$($a$){}_x=172$MPa,${}_y=103$MPa

$($b$){}_x=-105$MPa,${}_y=70$MPa,${}_{xy}=-105$MPa