(I have underlined any keywords in this response)
Break this question down into 2 halves to make it easier to answer:
2. "Explain how a plant root hair cell uses this to facilitate uptake of nutrients from the soil.": (facilitate is just a nasty word for 'carry out'). Root hair cells contain carrier proteins, which allow the cell to take up specific molecules from the soil and transport them againt the concentration gradient through the plant cell membrane. The carrier protein uses the energy molecule, ATP to grab nutrients (e.g nitrates) from the soil and release them into the cell, in which there is already a high concentration.