$ 
$$$76. Given a point 
. Find the coordinates of the point С, делящей отрезок АВ with respect to 
$$ 
$ 
$ 
$ 
$$$77. Determine the distance between two lines: 
and 
$$ 
$ 
$ 2
$ 5
$$$78. Find 
, if 
.
$$ 
$ 
$ 
$ 
$$$79. Find 
, if 
.
$$ 
$ 6
$ 
$ 16
$$$80. Force 
is applied to the point 
. Determine the moment of force about a point 
.
$$ 
$ 
$ 
$ 
$$$81. Show the condition of parallelism of lines: 
$$ 
$ 
$ 
$ 
$$$82. Given that two points 
. Find the coordinates of the mid-point АВ.
$$ 
$ 
$ 
$ 
$$$83. Write an equation of the line that passes through the point 
and has slope 
.
$$ 
$ 
$ 
$ 
$$$84. Find the vector 
with given coordinates of head and tail 
and 
.
$$ 
$ 
$ 
$ 
$$$85. Find the distance from the point 
to the point 
.
$$ 
$ 
$ 5
$ 0
$$$86. The rank of the matrix of the system equations 
equal to
$$ 2
$ 1
$ 0
$ 3
$$$87. The integrals with infinite limits 
is:
$$ improper integral
$ indefinite integral
$ integral sum
$ proper integral
$$$88. The rank of the augmented matrix for the system 
is equal to:
$$ 3
$ 2
$ 0
$ 1
$$$89. To bring the integral 
to the tabulated integral, the replacement must be done.
$$ 
$ 
$ 
$ 
$$$90. Given that formula 
...is called
$$ Newton-Leibniz formula.
$ Kroneccker-Capelli formula.
$ integrating by parts.
$ substitution of a variable.
$$$91. The triple product of the vectors 
is equal to
$$ 1
$ 3
$ 0
$ -1
$$$92. The triple product of the vectors 
:
$$ 3
$ 0
$ 5
$ 1
$$$93. Set, where the function 
is convex, has the form:
$$ 
$ 
$ 
$ 
$$$94. Canonical equation of a hyperbola with the semi-transverse axis Ox is
$$ 
$ 
$ 
$ 
$$$95. Determine the intervals of decrease for function: 
$$ 
$
$ 
$ 
$$$96. Find the integral: 
$$ 
$ 
$ 
$ 
$$$97. Given that 
$$ 
$ 
$ 
$ 
$$$98. If the functions 
and 
are differentiable, then 
$$ 
$ 
$ 
$ 
$$$99. Calculate the integral: 
$$ 
$ 
$ 
$ 
$$$100. The canonical equation of elliptical paraboloid is:
$$ 
$ 
$ 
$ 
$$$101. Find the intersection point of the line 
and the plane 
:
$$ 
$
$ 
$
$$$102. Find the limit: 
$$ 2
$ 
$ 1
$ 
$$$103. Find the second derivative of the function 
.
$$ 
$ cosx
$ cos2x
$ 2cosx
$$$104. Given that 
, 
. Find the coordinates of the mid-point АВ.
$$ 
$
$ 
$
$$$105.The two vectors 
and 
will be collinear, if the condition is:
$$ 
$ 
$ 
$ 
$$$106. Given the two vectors 
and 
. At what «m» and «k», these vectors are collinear:
$$ 
$ 
$ 
$ 
$$$107. Find the area of the parallelogram constructed on vectors 
, if 
and corner between the vectors 
.
$$ 
$40
$20
$-6
$$$108. At what «k» vectors 
and 
are orthogonal?
$$ -3
$ 7
$ 5
$ 2
$$$109. Find the cosine of the angle between vectors 
.
$$0
$1
$-1
$1/2
$$$110. The rank of a matrix is equal to zero if and only if:
$$ all elements of matrix equal to zero
$ identity matrix
$ invertible matrix
$ matrix contains a null string
$$$111. Which of the following lines will be parallel?
1) 
; 2) 
3) 
; 4) 
.
$$ 1 и 2
$ 1 и 3
$ 2 и 3
$ 2 и 4
$$$112. Which of the following planes pass through the origin of coordinates?
1) 
; 2) 
; 3) 
; 4) 
?
$$ 2
$1
$ 1 и 4
$ 2 и 3
$$$113. The volume of a pyramid, constructed on the vectors 
is equal
$$ 
$ 
$ 
$ 
$$$114. If 
, 
is the point of discontinuity … of function 
.
$$ first type
$ second type
$ extreme point
$ continuity
$$$115. If n1 and n2 – normal vectors of 2-planes, than condition of perpendicularity of the planes has the form:
$$ 
$ 
$ 
$ 
$$$116. A whole of definite, distinct objects gathered together according to some criterion, are called…
$$ set
$ object
$ number
$ subset
$$$117. Find the coordinates of the center of the circle: 
$$ 
$
$
$ 
$$$118. Find semi-axis of the ellipse 
$$ 3 и 2
$ 2 и 3
$ 2 и 6
$ 6 и 3
$$$119. Find semi-axis of the hyperbola 
$$ 1 и 3
$ 3 и 0
$ 0 и 3
$ 1 и 1
$$$120. Find the distance between two points 
and 
.
$$ 
$ 0
$ -1
$ 
$$$121. Find the coordinates of the projection of 
on plane ОХУ.
$$ 
$
$
$
$$$122. If a plane parallel to the plane УОZ, than general equation of the plane has the form:
$$ 
$ 
$ 
$ 
$$$123. The slope of the line is equal to
$$ 5
$ -5
$ 3
$ -1
$$$124. Find y-intercept of the line 
.
$$ 5
$ 1
$ -2
$ -5
$$$125. Given that 
. Determine the coordinates 
.
$$ 
$
$ 
$
$$$126. A basis is …
$$ a set of linearly independent vectors that can represent every vector.
$ a set of linearly dependent vectors that can represent every vector.
$ a set of vectors that can represent every vector.
$ a linearly dependent vectors.
$$$127. The length of the interval 
between the base of the perpendiculars from points A and B on the axis L is
$$ projection of the vector а, on the axis L.
$ basis vectors.
$ corner.
$ distance.
$$$128. Vectors are … if they lie in the same plane or in parallel planes
$$ complanar
$ intersected
$ equal
$ perpendicular
$$$129. If there exists a number 
such that all values 
fall within the interval 
, then the variable is called
$$ bounded
$ constant
$ even
$ monotonous
$$$130. Linear operations on vectors are:
$$ addition, subtraction, multiply by a number
$ addition, subtraction, division
$ addition, division
$ subtraction, division, multiply by a number
$$$131. Find the coordinates of diagonals of the parallelogram which is resultant of two vectors 
$$ 
$ 
$ 
$ 
$$$132. The ratio 
of half the distance between the foci of the ellipse semi-major axis is:
$$ an eccentricity
$ a focus
$ a directrixs
$ an asymptote
$$$133. Find the distance from the point 
to the plane 
$$ 
$ 
$ 
$ 
$$$134. Write an equation of the plane which have a normal vector and passing through the point 
:
$$ 
$ 
$ 
$ 
$$$135. The condition for two planes 
and 
to be perpendicular is:
$$
$ 
$ 
$ 
$$$136. The condition for two planes and to be parallel is:
$$
$
$ 
$
$$$137. The three-intercept equation of a plane is
$$
$
$ 
$
$$$138. Find the distance 
from the point 
to the plane 
:
$$ 
$ 
$ 
$ 
$$$139. Find the limit: 
.
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