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**1. Homework Statement**

The components of stress in the [itex]x_i[/itex] reference Cartesian system at a point of interested have been determined to be:

[itex]

\left[\begin{array}{ccc}

500 & 0 & 300 \\

0 & 700 & 0 \\

300 & 0 & -100

\end{array}\right] \mathrm{MPa}

[/itex]

Determine the principal values and directions of stress. Determine the rotation tensor transforming the components of stress from the principal components into components along the [itex]x_i[/itex] reference Cartesian system.

**2. Homework Equations**

[itex]\mathbf{A} = \mathbf{R}^T \mathbf{V} \mathbf{R}[/itex]

where [itex]\mathbf{A}[/itex] is the original stress tensor, [itex]\mathbf{R}[/itex] is the rotation tensor, and [itex]\mathbf{V}[/itex] is a matrix of eigenvectors.

**3. The Attempt at a Solution**

I've solved for the principal values and directions, but don't know how to solve for the rotation tensor. It seems there's too many unknowns or I'm not making a necessary assumption. Does anyone have any suggestions?

Thank You.