Answer:
The gravitational potential energy equals the work needed to lift the object.
Explanation:
here we know that
work done is given as
Potential energy is given as
force due to gravity is given as
now here if we plug in the value of distance and force in the formula of work done then we will have
so here we got
so we can concluded that
The gravitational potential energy equals the work needed to lift the object.
Answer:
A. False
B. False
C. True
D. True
E. True
F. True
Explanation:
A. The equation Ax=b is referred to as a matrix equation and not vector equation.
B. If the augmented matrix [ A b ] has a pivot position in every row then equation Ax=b may or may not be consistent. It is inconsistent if [A b] has a pivot in the last column b and it is consistent if the matrix A has a pivot in every row.
C. In the product of Ax also called the dot product the first entry is a sum of products. For example the the product of Ax where A has [a11 a12 a13] in the first entry of each column and the corresponding entries in x are [x1 x2 x3] then the first entry in the product is the sum of products i.e. a11x1 + a12x2 +a13x3
D. If the columns of mxn matrix A span R^m, this states that every possible vector b in R^m is a linear combination of the columns which makes the equation consistent. So the equation Ax=b has at least one solution for each b in R^m.
E. It is stated that a vector equation x1a1 + x2a2 + x3a3 + ... + xnan = b has the same solution set as that of the linear system with augmented matrix [a1 a2 ... an b]. So the solution set of linear system whose augmented matrix is [a1 a2 a3 b] is the same as solution set of Ax=b if A=[a1 a2 a3] and b can be produced by linear combination of a1 a2 a3 iff the solution of linear system corresponding to [a1 a2 a3 b] takes place.
F. It is true because lets say b is a vector in R^m which is not in the span of the columns. b cannot be obtained for some x which belongs to R^m as b = Ax. So Ax=b is inconsistent for some b in R^m and has no solution.
From the conservation of linear momentum of closed system,
Initial momentum = final momentum
Mass of the student, M = 59 kg
Mass of the laser boat, m = 42 kg
Initial speed of student + laser boat, u =0
Final speed of laser boat, v = 1.5 m/s
Final speed of the student = V
(M+m) u =M V +m v
0 = (59 kg) V + (42 kg) (1.5m/s)
V = - 1.06 m/s
Thus, the speed of the student is 1.06 m/s in the opposite direction of the motion of boat.
Answer:
hydrogen bridge
Explanation:
Joule's relationship to heat and temperature is true for all materials where we assume that interatomic forces are linear, when atoms separate these forces decrease. There is a point where the separation between atoms is enough that thermal agitation can separate the molecules and there is a change of state, generally from solid to liquid and from liquid to vapor. When these changes of state are occurring all the energy supplied is used to break the links, so the temperature does not change.
In the specific case of water, there is a bond called a hydrogen bridge that breaks around 4ºC, therefore, at this temperature there is a deviation from the curve since this link is being broken, this does not lead to a change of macroscopic state.
For the other temperatures the water behaves like the other bodies.
Answer: liquids take the shape of the container they are in, but have definite volume. like liquids the shape of a gas changes with the container. unlike liquids the volume of a gas changes depending on the container it is in
Explanation:
