Nitrogen from the air is a key component in the industrial manufacture of ammonia (NH\(_3\)) through the Haber process, which is then used as a primary material in the production of nitric acid (HNO\(_3\)) - Option C

A. production of cooling agent: While liquid nitrogen is an excellent cooling agent (refrigerant), this is a use of the separated gas and not a large-scale process for which nitrogen is primarily sourced from the air in the context of the other options provided. The main large-scale use is chemical manufacturing.

B. production of margarine: Margarine is made from vegetable oils and water, sometimes involving hydrogenation processes, but nitrogen itself is not a primary component in its manufacture, though it may be used in food packaging to prevent oxidation.

D. manufacturing of oil: Nitrogen is not used to manufacture oil. It is used as an inert atmosphere in various industrial processes, including potentially parts of the petrochemical industry, but not the synthesis of oil itself.