let
Q(sqrt(2),sqrt(3)) be the field generated by elements of the form
a+bsqrt(2)+csqrt(3)+dsqrt(6) where a,b,c,d are in
Q(sqrt(2),sqrt(3)) is a vector space of dimension 4 over A. find a
basis for Q(sqrt(2),sqrt(3))
prove that where a,b,c,d,e are real numbers with (a) not equal
to zero. if this linear equation ax+by=c has the same solution set
as this one : ax+dy=e, then they are the same equation.
Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are
all real numbers
(a) Derive an equation for a line tangent to both of these
parabolas (show all steps with a proof, assuming that such
a line exists)
(b) Assume that the doubly-tangent line has an equation y+Ax+B.
Find an example of values of a,b,c (other than the ones given here)
such that A,B ∈ Z
1. Evaluate: (a+b)/(c-d) + 9/(a+d) when a=5,
b=3, c=8, d=4
a. 6
b. 3
c. 15/2
d. 17/13
2. Solve for x: 5(x+3) = 35
a. 2
b. 7
c. 4
d. -4
3. Acid rain occurs primarily as a result of
a. operating a nuclear power plant
b. burning coal or oil containing sulfur
c. by-products created by operating an oil refinery
d. the use of Freon and other refrigerants
4. The "ozone holes" at the polar region arise...
2. Define a relation R on pairs of real numbers as follows: (a,
b)R(c, d) iff either a < c or both a = c and b ≤ d. Is R a
partial order? Why or why not? If R is a partial order, draw a
diagram of some of its elements.
3. Define a relation R on integers as follows: mRn iff m + n is
even. Is R a partial order? Why or why not? If R is...
3. Where in the cell does TRANSCRIPTION
occur?
A. nucleus B. mitochondria C. chloroplast D. All of the
above
9. mRNAs usually have a start translation site of AUG.
true or false?
16. Which type of RNA makes up the
spliceosome?
A. rRNA B. snRNA C. tRNA D. snRNPs E. siRNAs
17. Which type of PROTEINS help make up the
spliceosome?
A. rRNA B. snRNA C. tRNA D. snRNPs E. siRNAs
25. Introns have conserved sequences that help to orient...