Consider a wire in the shape of a helix $\mathbf{r}(t) = 2 \cos t \mathbf i + 2 \sin t \mathbf j + 5 t \mathbf k, 0 \leq t \leq 2\pi$ with constant density function $\rho(x, y, z) = 1$.

A. Determine the mass of the wire:

B. Determine the coordinates of the center of mass: (, , )

C. Determine the moment of inertia about the z-axis:
Note: If a wire with linear density $\rho(x, y, z)$ lies along a space curve $C$, its moment of inertia about the z-axis is defined by $I_z = \int_C (x^2+y^2) \rho(x, y, z) ds$.