We observe a distant object in space and see that the spectral lines for hydrogen in the object's light appear at a shorter wavelength than normal. What does this tell us about the object

This tells us the radial velocity of the object and that the object is approaching or coming towards us.

Explanation:

Certain chemicals radiate with particular wavelengths or colors  when their temperature is raised or when they are charged electrically. Also observable are dark strokes separating the spectrum known as absorption lines

These spectral lines of chemicals are well known as stated above and from the phenomenon of Doppler effect, spectroscopy can be used to detect the movement of a distant object by the change of the emitted frequency of the wavelength

The Doppler effect is used in calculating the radial velocity of a distant object due to the fact that an approaching object compresses its emitted signal wavelength while a receding object has a longer wavelength than normal

2fe + 3h2so4 -> fe2(so4)3 + 3h2

it is necessary to balance equations in order to get the proper amount of reactants as well as products in order not to make a miscalculation.

you cannot change the subscripts as that would change the substance itself. for instance, diatomic elements such as h2 only have the subscript two when a gas. another example would be so4, if you were to change the subscript, the element would no longer be sulfate.

we change the coefficients instead as that only changes the number of molecules rather than the substance itself.

hope this !