Two vectors are given by \(\overrightarrow{\mathbf{A}}=4.0 \hat{\mathbf{x}}-2.0 \hat{\mathbf{y}}\) and \(\overrightarrow{\mathbf{B}}=1.0 \hat{\mathbf{x}}+5.0 \hat{\mathbf{y}}\). What is (a) \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}\), (b) \(\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}\), and (c) a vector \(\overrightarrow{\mathbf{C}}\) such that \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{C}}=0\) ?