1.11.10 Tensor calculus

Problem: Given the permittivity tensor: \( \varepsilon_{i j}= \) \( \left(\begin{array}{ccc}3 & 2 & 0 \\ 2 & 4 & -2 \\ 0 & -2 & 5\end{array}\right) \), the material is placed in a uniform field with intensity \( E=E_{0}\{-2 ; 2 ; 1\} \). Find: 1) dielectric susceptibility tensor \( \alpha_{i j} \) of dielectric 2) polarization vector \( P \), 3) electric induction vector \( D \), 4) pairwise angles between vectors \( E, P, D \).