\begin{tikzpicture}[scale=2.5, vec/.style={-{Latex[length=3mm]}, thick}, >=Latex]
  % axes
  \draw[gray, ->] (-1.3,0) -- (1.6,0) node[right] {$x$};
  \draw[gray, ->] (0,-0.3) -- (0,1.7) node[above] {$y$};

  % original square (dashed)
  \draw[dashed, thick, gray] (0,0) -- (1,0) -- (1,1) -- (0,1) -- cycle;
  \node[gray] at (0.5,-0.18) {original};

  % rotated square (solid, colored) by 45 degrees
  \draw[thick, red!70!black, fill=red!10, fill opacity=0.4]
    (0,0) -- (0.7071,0.7071) -- (0,1.4142) -- (-0.7071,0.7071) -- cycle;
  \node[red!70!black] at (0,1.6) {$45^\circ$};

  % angle arc
  \draw[->, thick] (0.5,0) arc (0:45:0.5);
\end{tikzpicture}