Is there a surface S$\subset R^3$ whose Gaussian curvature is -1 at each point S?

Question

Is there a surface $S\subset \Bbb R^3$ whose Gaussian curvature is $-1$ at each point $S$?

At first I think this does not make a sense.

But googling and googling.. I found a 'final exam problem'

https://www.ma.utexas.edu/users/dafr/M365G/Final_soln.pdf

question no.$7$ says my question is TRUE..

How can I think the surface whose Gaussian curvature is $-1$ every point.

And is there a surface whose Gaussian curvature is constant $K<0$??

Thanks for reading my question.