show that for any two vectors u and v in an inner product space

||u+v||^2+||u-v||^2=2(||u||^2+||v||^2)

give a geometric interpretation of this result fot he vector space R^2

Calculus dictates that
(∂U/∂V) T,Ni = T(∂S/∂V)T,Ni – p = T(∂p/∂T)V,Ni – p

(a) Calculate (∂U/∂V) T,N for an ideal gas [ for which p = nRT/V ]

(b) Calculate (∂U/∂V) T,N for a van der Waals gas
[ for which p = nRT/(V–nb) – a (n/V)2 ]

(c) Give a physical explanation for the difference between the two.

(Note: Since the mole number n is just the particle number N divided by Avogadro’s number, holding one constant is equivalent to holding the other constant.)

I have attached the following script file

Q1) List the full name of members, their DETAIL_DAILYLATEFEE and the average of DETAIL_DAILYLATEFEE for all members whose DETAIL_DAILYLATEFEE is less than the average of all DETAIL_DAILYLATEFEE.
Your query MUST contain a subquery.
Your result should be as shown below. Note that each member is only listed once.
Required: AVG(DETAIL_DAILYLATEFEE)
CONCAT
DISTINCT
Restricted: GROUP BY

Q2) Management is also interested in finding out the age of their movies (i.e. how old the movies are) in number of years compared to the average age (in rounded number of years) of all movies in their stock. They want a report that lists information about the title, year, genre and how many 'Years Old' a movie is, for all movies that are newer than the average age (in rounded years) of all movies. (For example, if the average age of all movies is X, list all movies with age < X)  
Required:
ROUND(AVG(MOVIE_YEAR))
YEAR(NOW()) - MOVIE_YEAR

-- Comment the following two lines if creating database in Mimir or Bluenose
create schema if not exists DVD_vidrental;
use DVD_vidrental;

DROP TABLE IF EXISTS `detailrental`;
DROP TABLE IF EXISTS `rental`;
DROP TABLE IF EXISTS `video`;
DROP TABLE IF EXISTS `movie`;
DROP TABLE IF EXISTS `price`;
DROP TABLE IF EXISTS `membership`;

CREATE TABLE `membership` (
`MEM_NUM` decimal(8,0) NOT NULL,
`MEM_FNAME` varchar(30) NOT NULL,
`MEM_LNAME` varchar(30) NOT NULL,
`MEM_STREET` varchar(120) DEFAULT NULL,
`MEM_CITY` varchar(50) DEFAULT NULL,
`MEM_STATE` char(2) DEFAULT NULL,
`MEM_ZIP` char(5) DEFAULT NULL,
`MEM_BALANCE` decimal(10,2) DEFAULT NULL,
PRIMARY KEY (`MEM_NUM`)
);

CREATE TABLE `price` (
`PRICE_CODE` decimal(2,0) NOT NULL,
`PRICE_DESCRIPTION` varchar(20) NOT NULL,
`PRICE_RENTFEE` decimal(5,2) DEFAULT NULL,
`PRICE_DAILYLATEFEE` decimal(5,2) DEFAULT NULL,
PRIMARY KEY (`PRICE_CODE`)
);

CREATE TABLE `movie` (
`MOVIE_NUM` decimal(8,0) NOT NULL,
`MOVIE_TITLE` varchar(75) NOT NULL,
`MOVIE_YEAR` decimal(4,0) DEFAULT NULL,
`MOVIE_COST` decimal(5,2) DEFAULT NULL,
`MOVIE_GENRE` varchar(50) DEFAULT NULL,
`PRICE_CODE` decimal(2,0) DEFAULT NULL,
PRIMARY KEY (`MOVIE_NUM`),
KEY `PRICE_CODE` (`PRICE_CODE`),
CONSTRAINT `movie_ibfk_1` FOREIGN KEY (`PRICE_CODE`) REFERENCES `price` (`PRICE_CODE`)
);

CREATE TABLE `video` (
`VID_NUM` decimal(8,0) NOT NULL,
`VID_INDATE` date DEFAULT NULL,
`MOVIE_NUM` decimal(8,0) DEFAULT NULL,
PRIMARY KEY (`VID_NUM`),
KEY `MOVIE_NUM` (`MOVIE_NUM`),
CONSTRAINT `video_ibfk_1` FOREIGN KEY (`MOVIE_NUM`) REFERENCES `movie` (`MOVIE_NUM`)
);

CREATE TABLE `rental` (
`RENT_NUM` decimal(8,0) NOT NULL,
`RENT_DATE` date DEFAULT NULL,
`MEM_NUM` decimal(8,0) DEFAULT NULL,
PRIMARY KEY (`RENT_NUM`),
KEY `MEM_NUM` (`MEM_NUM`),
CONSTRAINT `rental_ibfk_1` FOREIGN KEY (`MEM_NUM`) REFERENCES `membership` (`MEM_NUM`)
);

CREATE TABLE `detailrental` (
`RENT_NUM` decimal(8,0) NOT NULL,
`VID_NUM` decimal(8,0) NOT NULL,
`DETAIL_FEE` decimal(5,2) DEFAULT NULL,
`DETAIL_DUEDATE` date DEFAULT NULL,
`DETAIL_RETURNDATE` date DEFAULT NULL,
`DETAIL_DAILYLATEFEE` decimal(5,2) DEFAULT NULL,
PRIMARY KEY (`RENT_NUM`,`VID_NUM`),
KEY `VID_NUM` (`VID_NUM`),
CONSTRAINT `detailrental_ibfk_1` FOREIGN KEY (`RENT_NUM`) REFERENCES `rental` (`RENT_NUM`),
CONSTRAINT `detailrental_ibfk_2` FOREIGN KEY (`VID_NUM`) REFERENCES `video` (`VID_NUM`)
);

START TRANSACTION;

INSERT INTO `membership` VALUES (102,'TAMI','DAWSON','2632 TAKLI CIRCLE','NORENE','TN','37136',11.00),
(103,'CURT','KNIGHT','4025 CORNELL COURT','FLATGAP','KY','41219',6.00),
(104,'JAMAL','MELENDEZ','788 EAST 145TH AVENUE','QUEBECK','TN','38579',0.00),
(105,'IVA','MCCLAIN','6045 MUSKET BALL CIRCLE','SUMMIT','KY','42783',15.00),
(106,'MIRANDA','PARKS','4469 MAXWELL PLACE','GERMANTOWN','TN','38183',0.00),
(107,'ROSARIO','ELLIOTT','7578 DANNER AVENUE','COLUMBIA','TN','38402',5.00),
(108,'MATTIE','GUY','4390 EVERGREEN STREET','LILY','KY','40740',0.00),
(109,'CLINT','OCHOA','1711 ELM STREET','GREENEVILLE','TN','37745',10.00),
(110,'LEWIS','ROSALES','4524 SOUTHWIND CIRCLE','COUNCE','TN','38326',0.00),
(111,'STACY','MANN','2789 EAST COOK AVENUE','MURFREESBORO','TN','37132',8.00),
(112,'LUIS','TRUJILLO','7267 MELVIN AVENUE','HEISKELL','TN','37754',3.00),
(113,'MINNIE','GONZALES','6430 VASILI DRIVE','WILLISTON','TN','38076',0.00);

INSERT INTO `price` VALUES (1,'Standard',3.00,1.00),
(2,'New Release',4.50,3.00),(3,'Discount',2.50,1.00),
(4,'Weekly Special',2.00,0.50);
INSERT INTO `movie` VALUES (1234,'The Cesar Family Christmas',2014,39.95,'FAMILY',2),
(1235,'Smokey Mountain Wildlife',2011,59.95,'ACTION',3),(1236,'Richard Goodhope',2015,59.95,'DRAMA',2),
(1237,'Beatnik Fever',2014,29.95,'COMEDY',2),(1238,'Constant Companion',2015,89.95,'DRAMA',NULL),
(1239,'Where Hope Dies',2005,25.49,'DRAMA',3),(1245,'Time to Burn',2015,45.49,'ACTION',3),
(1246,'What He Doesn\'t Know',2013,58.29,'COMEDY',1);
INSERT INTO `video` VALUES (34341,'2014-01-22',1235),(34342,'2014-01-22',1235),
(34366,'2016-03-02',1236),(34367,'2016-03-02',1236),(34368,'2016-03-02',1236),
(34369,'2016-03-02',1236),(44392,'2015-10-21',1237),(44397,'2015-10-21',1237),
(54321,'2015-06-18',1234),(54324,'2015-06-18',1234),(54325,'2015-06-18',1234),
(59237,'2016-02-14',1237),(61353,'2013-01-28',1245),(61354,'2013-01-28',1245),
(61367,'2015-07-30',1246),(61369,'2015-07-30',1246),(61388,'2014-01-25',1239);
INSERT INTO `rental` VALUES (1001,'2016-03-01',103),(1002,'2016-03-01',105),
(1003,'2016-03-02',102),(1004,'2016-03-02',110),(1005,'2016-03-02',111),
(1006,'2016-03-02',107),(1007,'2016-03-02',104),(1008,'2016-03-03',105),(1009,'2016-03-03',111);
INSERT INTO `detailrental` VALUES (1001,34342,2.00,'2016-03-04','2016-03-02',NULL),
(1001,34366,3.50,'2016-03-04','2016-03-02',3.00),(1001,61353,2.00,'2016-03-04','2016-03-03',1.00),
(1002,59237,3.50,'2016-03-04','2016-03-04',3.00),(1003,54325,3.50,'2016-03-04','2016-03-09',3.00),
(1003,61369,2.00,'2016-03-06','2016-03-09',1.00),(1003,61388,0.00,'2016-03-06','2016-03-09',1.00),
(1004,34341,2.00,'2016-03-07','2016-03-07',1.00),(1004,34367,3.50,'2016-03-05','2016-03-07',3.00),
(1004,44392,3.50,'2016-03-05','2016-03-07',3.00),(1005,34342,2.00,'2016-03-07','2016-03-05',1.00),
(1005,44397,3.50,'2016-03-05','2016-03-05',3.00),(1006,34366,3.50,'2016-03-05','2016-03-04',3.00),
(1006,61367,2.00,'2016-03-07',NULL,1.00),(1007,34368,3.50,'2016-03-05',NULL,3.00),
(1008,34369,3.50,'2016-03-05','2016-03-05',3.00),
(1009,54324,3.50,'2016-03-05',NULL,3.00);

COMMIT;

In the experiment: To determine the resistivity of a semiconductor using Four probe method.

What does the floating potential mean? Like what's the difference between potential and floating potential?

Also what does the correction factor in this experiment signify? Like why do we need the correction factor in this experiment?
The value of the correction factor in this experiment is G7 which is 2ln2.

The Cauchy-Schwarz Inequality Let u and v be vectors in R 2 .

We wish to prove that ->    (u · v)^ 2 ≤ |u|^ 2 |v|^2 .

This inequality is called the Cauchy-Schwarz inequality and is one of the most important inequalities in linear algebra.

One way to do this to use the angle relation of the dot product (do it!). Another way is a bit longer, but can be considered an application of optimization. First, assume that the two vectors are unit in size and consider the constrained optimization problem:

Maximize u · v

Subject to |u| = 1 |v| = 1.

Note that |u| = 1 is equivalent to |u| 2 = u · u = 1.

(a) Let u = a b and v = c d . Rewrite the above maximization problem in terms of a, b, c, d.

(b) Use Lagrange multipliers to show that u · v is maximized provided u = v.

(c) Explain why the maximum value of u · v must, therefore, be 1.

(d) Find the minimum value of u · v and explain why for any unit vectors u and v we must have |u · v| ≤ 1.

(e) Let u and v be any vectors in R 2 (not necessarily unit). Apply your conclusion above to the vectors: u |u| and v |v| to show that (u · v) ^2 ≤ |u|^ 2 |v|^ 2 .

A basis of a vector space V is a maximal linearly independent set of vectors in V . Similarly, one can view it as a minimal spanning set of vectors in V . Prove that any set S ⊆ V spanning a finite-dimensional vector space V contains a basis of V .

In one or two paragraphs, write your opinion about what the author discusses: do you agree with his argument? In other words, do you think the convergence of global accounting systems is necessary? or could it be harmful? Why? Comparing GAAP & IFRS

1. Define the term break-even point.
2. What is the variable cost ratio? The contribution margin ratio? How are the two ratios related?
3. Define the term sales mix. Give an example to support your definition.
4. Cite and give credit to the author that you are citing

On average a textbook author makes two word processing errors per page on the first draft of her textbook. Assuming the errors per page are distributed as Poisson, what is the probability that on the next page she will make:

a) 2 or more errors?

b) No errors?

1. Define the term break-even point.
2. What is the variable cost ratio? The contribution margin ratio? How are the two ratios related?
3. Define the term sales mix. Give an example to support your definition.
4. Cite and give credit to the author that you are citing