Problem $3.$ A material point has the following stress components: ${}_x=200k,{}_y=-120k,$

${}_z=100k,{}_{xy}=80k,{}_{yz}=0k,{}_{zx}=0k.$ A new coordinate system is obtained by

rotating the old coordinate system about the $z-$axis clockwise by $75.$ Find the stress components

in the new coordinate system.

Problem $4.$ For the stress state given in Problem $3,$ find the principal stresses and the

corresponding principal directions.