What invention provided factories with hydropower?

The answer is Arkwright’s water frame. This invention is patented by Richard Arkwright in 1768 based on Thomas Highs, the water frame if for the spinning of the frame and the water power is used to make it move. This is used flowing water as its source of power. 

newly independent countries of the former ussr

the correct answer is b) the american colonies were not supporting each other.

at the time abigail wrote her second letter to john adams on november 27, 1775 she begins the letter with a series of rhetorical questions such as: if a form of government is to be established here what one will be assumed? , will it be left to the assemblies to chose one? with this questions, she is asking her husband what new form of government will be established and she is concerned that the delegates may not be able to come to consensus.

also, abigail believes that the regulations of government have been "so long slackened" that people could ignore a new government; she recognizes difficulty to establishing a new state.