Evaluate $\lceil (3.6)^2 \rceil - ( \lceil 3.6 \rceil ) ^2$.
I see some ceiling functions here, which round up to the nearest integer. So I need to be careful about what they do to the numbers inside them. Let me start by evaluating the inner expressions. $(3.6)^2$ is $12.96$, and $\lceil 3.6 \rceil$ is $4$. Now I need to apply the ceiling functions to these results. $\lceil 12.96 \rceil$ is $13$, and $(\lceil 3.6 \rceil)^2$ is $4^2$, which is $16$. Finally, I need to subtract these two values. $13 - 16$ is $-3$. 