When applying to Cornell, you will select a specific college, from the College of Arts and Sciences to the College of Engineering to the College of Agriculture. For the College of Arts and Sciences -- the largest undergraduate college at Cornell -- 2 SAT Subject Tests are required in addition to the SAT or ACT. For the College of Engineering, 2 Subject Tests are required as well, but they must be in math (any level) and a science. Architecture, Art, and Planning as well as Hotel Administration require an SAT Subject Test in math. The other schools do not require subject tests. You can view a full chart of the various colleges' testing requirements here.
A common component of the academic job application is the Research Statement (or Statement of Research Interests). This statement provides a summary of your research accomplishments and current work and discusses the future direction and potential of your work. The statement can discuss specific issues such as funding history and potential, requirements for laboratory equipment and space, and potential research and industrial collaborations. It should be technical, but should remain intelligible to any member of the department. Because it has the potential to be read by people outside of your subdiscipline, the "big picture" is important to keep in mind. The strongest research statements present a readable, compelling, and realistic research agenda that fits well with the needs, facilities, and goals of the department. Research statements can be weakened by overly ambitious proposals, by lack of clear direction, by lack of big-picture focus, or if inadequate attention is given to the needs and facilities of the department or position.