An astronaut holds a rock 100m above the surface of Planet X . The rock is then thrown upward with a speed of 15m/s , as shown in the figure. The rock reaches the ground 10s after it is thrown. The atmosphere of Planet X has a negligible effect on the rock when it is in free fall.

Explanation:

The described situation is is related to vertical motion (and free fall). So, we can use the following equation that models what happens with this rock:

(1)

Where:

is the rock's final height

is the rock's initial height

is the rock's initial velocity

is the angle at which the rock was thrown (directly upwards)

is the time

is the acceleration due gravity in Planet X

Then, isolating and taking into account :

(2)

(3)

Finally:

(4) This is the acceleration due gravity in Planet X

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.