Should you use hot or cold air to remove condensation from a car windshield in the winter?
Condensation on windshields forms when warm moist air comes in contact with a colder surface. In the winter, the interior of surface of your windshield is colder than the moist air leaving your lungs. When that air gets near the cold windshield, the water from the air condenses on the cold surface. If you were to heat the windshield, this temperature differential would decrease and in turn, so would condensation.
Explain a common problem when using the Newton-Raphson method of root finding.
Care must always be taken when choosing an initial guess of a root when using the Newton-Raphson method. Choosing a starting point too far from the desired root can cause the method to search in the wrong place or never find a root. In some unique cases it can cause a continuous cycle of incorrect roots (as in the equation y=x^3-2x+2.
Is it possible to generate lift with a perfectly symmetrical airfoil?
The answer, as are most answers in engineering, is "it depends!" Lift is generated when the air flow over the top of an air foil is faster than the air flow underneath, creating a low pressure area on the of top of the air foil and a higher pressure area underneath. This lower pressure area tries to pull to airfoil up, like a vacuum. Typical airfoils are asymmetric so that they can generate lift in steady flight while pointed directly at the air flow vector. A symmetrical airfoil (like those on acrobatic planes) must be inclined such that the stagnation point of the airflow vector is slightly below the leading edge of the wing in order to achieve the same type of pressure differential. This type of airfoil is advantageous for flying upside down because the wing can generate lift in any orientation just by adjusting its angle of attack to the velocity vector.