Question
Answer the following about the Joukowski transform, for 10 points each.
[10e] It maps one of these shapes onto the shape of an airfoil. The "unit" type of this shape is given the complex equation "modulus of z equals 1," or by the polar equation "r equals 1."
ANSWER: circle [or unit circle]
[10h] The Joukowski transform has this property, because it preserves the angles between intersecting curves. The Mercator map projection has this property, which means that straight lines on it have constant bearing.
ANSWER: conformal transformation [or conformality; or conformal map; or conformal mapping]
[10m] The standard Joukowski transform maps the complex number z to the complex number "z plus this function of z." If and only if z lies on the unit circle, this function of z gives the complex conjugate of z.
ANSWER: 1 over z [or reciprocal of z or z to the power negative 1 or z to the power minus 1]
<Joseph Krol , Science - Other - Math Applied>
Summary
| 2023 NASAT | 06/17/2023 | Y | 9 | 16.67 | 100% | 44% | 22% |
Data
| California | Kentucky B | 10 | 10 | 0 | 20 |
| Illinois White | Maryland Gold | 10 | 0 | 0 | 10 |
| Asia A | Maryland Red | 10 | 10 | 10 | 30 |
| Kentucky A | Missouri B | 10 | 0 | 10 | 20 |
| New Jersey A | Missouri A | 10 | 0 | 10 | 20 |
| Arkansas | New Jersey B | 10 | 0 | 0 | 10 |
| Ohio | Liberia | 10 | 0 | 0 | 10 |
| Illinois Blue | Pennsylvania | 10 | 0 | 10 | 20 |
| Virginia | Asia B | 10 | 0 | 0 | 10 |