Using the Nernst equation:
$$E = E^{\circ} - \frac{RT}{nF}\ln Q = E^{\circ} - \frac{0.0592}{n}\log Q$$
For $\text{Zn} + \text{Cu}^{2+} \rightarrow \text{Zn}^{2+} + \text{Cu}$, $n = 2$
$$Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} = \frac{0.01}{1} = 0.01$$
$$E = 1.1 - \frac{0.0592}{2}\log(0.01) = 1.1 - 0.0296 \times (-2)$$
$$= 1.1 + 0.0592 = \boxed{1.1592 \text{ V}}$$