Astronomers are getting information about dark energy from
a the existence of dark matter
b the number of stars in the sky
c the fact that gases are in galaxies
d the shape of galaxies in cluster galaxies

The only way of telling about dark energy is our observation of how the universe has been expanding. It basically works the opposite as gravity, pushing things away from it. Thus, the closest answer would be D. The shape of galaxies in cluster galaxies.

D. The shape of galaxies in cluster galaxies

Explanation:

When the Universe began to expand, everything present in Universe began to move at a very high rate. This was concluded that some external force is working on it in order to pull these things. It was known  as the dark energy.

Thus the size and shape of galaxies is increasing because of this  dark energy, hence the study of change in shape and size of galaxy gives information about dark energy as it is constantly applying  force thus increasing the size.

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

the answer would be c