Let an \(x^{\prime} y^{\prime} z^{\prime}\) coordinate system be defined using the three principal directions obtained from problem 8. Determine the transformed stress matrix \([\boldsymbol{\sigma}]_{x^{\prime} y^{\prime} z^{\prime}}\) in the new coordinate system.

Data From Problem 8:

Determine the principal stresses and their associated directions, when the stress matrix at a point is given by

11 1 [6]=112 MPa. [121]