A made-up tea stall records the noon temperature and the cups of hot tea it sells on five days…

Step 1. Celsius. The means are $18.4\ ^\circ\text{C}$ and $45.4$ cups. $S_{xx} = 109.2$, $S_{yy} = 551.2$ and $S_{xy} = -244.8$. So $r = \dfrac{-244.8}{\sqrt{109.2 \times 551.2}} = -0.9978$.

Step 2. Fahrenheit. The temperatures become $53.6$, $59$, $64.4$, $71.6$ and $77\ ^\circ\text{F}$. Every deviation of $x$ is $1.8$ times as large, so $S_{xy}$ grows by $1.8$ and $\sqrt{S_{xx}}$ grows by $1.8$ too. The factors cancel: $r = -0.9978$.