(Solved): Let the components of the stress tensor at a point \( (A) \) be given in matrix form by: \[ \sigma_ ...

Let the components of the stress tensor at a point \( (A) \) be given in matrix form by: \[ \sigma_{A}=\left[\begin{array}{ccc} 55 & 35 & 0 \\ 35 & 55 & 0 \\ 0 & 0 & -10 \end{array}\right] \mathrm{MPa} \] Determine: 1. The stress vector on the plane passing at \( (A) \) and having the unit normal: \[ v=\frac{1}{7}\left[\begin{array}{lll} 2 & -3 & 6 \end{array}\right]^{\mathrm{T}} \] 2. The normal stress component \( \left(\sigma_{n}\right) \) and shear component \( \left(\sigma_{s}\right) \) on the same plane. 3. The safety factor using Tresca and von Mises criteria if the yield stress is \( \left(\sigma_{y}=110 \mathrm{MPa}\right) \), which criterion is more conservative?