When Herodotus says, "while they were ruled by tyrants, were not better in war than any of their neighbors, whereas, after they were freed from tyranny, they became the best by far. This proves that, when they were kept down, they were intentionally slacking, because they were working for a master, whereas when they had been set free, each one was eager to achieve something for himself," about whom is he speaking

The Athenians.

Explanation:

Herodotus was an ancient historian from Greece most famous for his book "The Histories" which details the origins and events of the Greco-Persian wars. He was also attributed to be the first writer to systematically investigate historical events.

In Book V of his "The Histories", he states how the Athenians began to gain strength and become more stronger and united when they were free of any ruler. The passage in the text is from the third paragraph from the last part of the fifth book. And that was how the Athenians had come to be the strong race they were when they were attacked by the Thebans. This book ends the 'introduction' to how the Greco-Persian war came about.

the correct answer would be:  

a. adverb phrase

b. the colonies must seek protection from other nations.