17.6  What distinguishes a "normal" galaxy with one we call "active"?

An active galaxy has a lot of matter interacting with the huge black hole at its center - evidence includes strong emission from the galaxy's center at all wavelengths, and jets of hot gas.  Normal galaxies lack such phenomena.

17.7 What evidence do we have that most galaxies are composed largely of dark matter?

Although most of the visible material in spiral galaxies is concentrated toward the center of the galaxy, the rotation curves for spiral galaxies do not show that stars move more and more slowly the farther they are from the center, which is what would be expected.  This is evidence for the presence of matter that we cannot observe which is primarily located around the outer edges of the galaxies in halos.  For elliptical galaxies, they need much more mass than is visible to hold on to large amounts of very hot gas.

17.15 Assume the Sun is located 27,000 LY (2.6 x 10¹⁷ km) from the center of the Milky Way, and is moving along a circular orbit at a speed of 220 km/s.  How long does it take our Solar System to make one complete circuit around our Galaxy?

The circumference of the Sun's orbit is 2 x pi x 2.6 x 10¹⁷ km = 1.63 x 10¹⁸ km.  At a speed of 220 km/s, it takes
1.63 x 10¹⁸ km / 220 km/s = 7.41 x 10¹⁵ s to complete one orbit.  7.41 x 10¹⁵ s x 1 h/3600 s x 1 d/24 h x 1 year/365 d = 234 million years.