Answer
No, they can't.
Work Step by Step
The measurements can precisely determine one or the other, but not both.
The product $\Delta p \Delta x$ is equal to or greater than $\hbar$.
The uncertainty principle relates the uncertainty in the measurement of momentum, $\Delta p$, the uncertainty in the measurement of position, $\Delta x$, and Planck's constant divided by $2 \pi$.
Both uncertainties cannot be zero.
This is discussed on pages 593-594.
