Problem $7\mathrm{.}4\mathrm{.}18.(9$th$)$

$$ An element in plane stress is subjected to stresses ${}_x,{}_y,$ and ${}_{xy}($see figure$).$ Using Mohr's circle, determine $($a$)$ the principal stresses and $($b$)$ the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.

${}_x=2900$kPa,${}_y=9100$kPa,${}_{xy}=-3750$kPa