The correct answer is A. The nucleus controls the cell's activity.
To arrive at this answer, you can eliminate options B, C, and D through the process of elimination.
Option B, "The nucleus identifies a cell as belonging to a plant," is incorrect because the presence of a nucleus does not distinguish a cell as belonging to a plant. Both plant and animal cells have a nucleus.
Option C, "The nucleus determines what substances enter and leave the cell," is incorrect because this function is primarily carried out by the cell membrane, not the nucleus. The cell membrane regulates the movement of substances in and out of the cell.
Option D, "The nucleus can be seen under a transmission electron microscope," is incorrect because the statement is about the ability to visualize the nucleus, rather than its function within the cell.
By the process of elimination, A remains as the correct answer. The nucleus is the control center of the cell, containing the cell's genetic information and coordinating its activities. It plays a crucial role in controlling gene expression, DNA replication, and the production of proteins.