Question

To determine the key, you will first need to rearrange the numbers into a 100 x 100 matrix, with the first 100 numbers as the first row.

a) True
b) False

Answer 1

The correctness of the statement about arranging numbers into a matrix is contextual and generally false. Vectors can form right angle triangles with their components, and the Pythagorean theorem is applicable for calculating the length of the resultant vector from perpendicular vectors; both statements are true. The assumption regarding the force applied to push a box up a ramp is false.

Step-by-step explanation:

The subject matter of the question relates to rearranging numbers into a matrix and determining the correctness of certain statements involving mathematical concepts like vectors and forces. To address the first part of the question (which lacks context), typically one would not need to rearrange numbers into a matrix to determine a key unless specified by a particular mathematical or computational problem. Therefore, without additional context, the statement is false.

In regards to vectors and forces, the following statements are clarified:

• A vector can indeed form the shape of a right angle triangle with its x and y components, which is true.
• The Pythagorean theorem can be used to calculate the length of the resultant vector when two vectors are at right angles to each other, also true.
• As for the last statement, the inference that a boy pushing a box up a ramp must be applying a force of exactly 100 N because the ramp is 1.0 m high and 3.0 m long is false. The actual force depends on other factors such as friction and efficiency.