Triangle \triangle A'B'C'△A ′
B
′
C
′
triangle, A, prime, B, prime, C, prime is the result of dilating \triangle ABC△ABCtriangle, A, B, C about point AAA by a scale factor of 333.

Determine whether each claim about the properties of \triangle ABC△ABCtriangle, A, B, C and \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is true or false.
The coordinates of AAA and A'A
′
A, prime are the same.

The lengths of \overline{AB}
AB
start overline, A, B, end overline and \overline{A'B'}
A
′
B
′

start overline, A, prime, B, prime, end overline are equal.

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?