I have a question on the wording of the task
Find in $R^2$ the Hausdorff distance $h(S_7(a),(-9)S_1(b))$, where $a(2,-1)^T, b(-1,3)^T$
The first object is a circle with radius $7$ centered at point $a$, but in the second circle $-9$ what does it refer to? Do I need to multiply the radius of the circle by $-9$ or what operation should I do?
It’s impossible to tell without the notation explicitly defined. However. A common use of the notation is as follows: If $X$ is a set, then $kX$ is the set $\{ k x : x \in X \}$.
So, in your problem, $-9 S_1(b) = \{ -9 x : x \text{ is a point of the unit circle centered at b} \}.$