How to find the eigenvalues and eigenvectors of the following real symmetric matrix that depends on a real variable $t > 0$ with $t\rightarrow 0$?
$$ A(t) = \begin{bmatrix} 1 & O(t^2) \\ O(t^2) & at^2 + O(t^3) \end{bmatrix} $$ where $a$ is a real constant, and $O(\cdot)$ is the big-O notation