9. (10 points) Let $F(x,y)=\dfrac{-2y}{x^2+y^2}\mathbf{i}+\dfrac{2x}{x^2+y^2}\mathbf{j}$ and let $D=\{(x,y)\mid x^2+y^2=9\}$. Find

$$\int_{\partial D}\mathbf{F}\cdot \mathbf{T}\,ds,$$

where we traverse the boundary $\partial D$ in the counterclockwise direction and $\mathbf{T}$ is the unit tangent vector.