For the given $3$D stress state, the non$-$zero stresses are given:

${}_{}=0$MPa

${}_{yy}=100$MPa

${}_{zz}=0$MPa

${}_{xy}=-60$MPa

${}_{zx}=35$MPa

a$)$ Write the $3$D stress tensor $($matrix$)$

b$)$ Calculate the invariants $I_1,I_2,I_3$ and write the characteristic equation $($why is this method better than

graphing the Mohr's circle for this situation?$)$

c$)$ Calculate the ordered principal stresses by solving the for the Eigen values

d$)$ Check your value in Matlab or other digital means

e$)$ Find the absolute maximum shear stress

f$)$ Draw the Mohr's circle after the principal stresses are determined. Do everything by hand please! Thank you :)