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POWERS OF 10
a videito EXPLANATORY
Powers of ten videos is one of the most famous scientists in history. Powers of ten means "powers of ten" and is a wonderful video. First we move away from a bucolic summer picnic in jumps of powers of ten: one meter, ten meters, a hundred meters, a thousand feet, until our galaxy disappears in the distance, then we move in jumps of powers of ten, until the world subatomic. The video was created in 1977 and the pictures alone are enough to understand the concept.

hope you enjoyed it, you understand now why this is called power operation is to multiply a number, called BASE, for itself many times as specified by the EXPONENT?

FOR STUDY Read the copied material below and do the exercises proposed. If you have any questions or doubts in formulating concrete that can help you, write it as comment and respond.

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EXERCISES Here some problems that you work with power.

regularidades_potencias

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History

The story of 1 Remember the first videito
? Which was in Portuguese and told the story of numbers and mathematics. Well, that was the first chapter of a total of seven.

finally found a version in Castilian!

addition is complete, a half hour film ... put out Lights! If you want to see in full screen you must click on the region of the screen that says "youtube."

I made this video playlist at myflashfetish.com

Chapter 2 tells how the Babylonians invented a way of writing numbers. Around 1200 BC.
They did it on plates of clay to endure. Even carved stones as seen in the images has given graciously of the Louvre Museum and The Museum of Iraq.

The symbols used to represent numbers 1 to 59 were those shown below. Try to find the stone!

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numbers Inverse of a Number - Multiplication and division



"All numbers are reversed? Is there any number multiplied by 0 to 1? Why? You

call rational numbers which can be written as a fraction. How is the inverse of a rational number?

Any number of form except zero, supports an inverse form

Copy in your notebook and complete the following table:



In the figure below two numbers are represented on a number line. One is the inverse of another.
moving the point called "number" answer the questions below.

Sorry, GeoGebra Applet can not start. Make sure you have Java 1.4.2 (or later) installed and activate JavaScript in your browser ( Click here to install Java now )

1) As the number increases, what about its opposite?

2) What is the opposite of 1?

3) Between which two numbers are the reciprocals of all numbers greater than 1?

4) What is the inverse of (-2)? Why?

5) What happens to the reciprocals of the numbers are between 0 and 1?

6) What are the signs of two opposite numbers?

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DIVISION negative numbers Addition and subtraction

Remember that when we work with natural numbers we define the multiplication as an addition in which all the summands are equal.




Let's see how to extend this reasoning to the numbers with signs.
First let's see if the addends are negative numbers would be:

Notes that, in this case, the factors have different signs and the product is a negative sign.

Based on the above two examples we can say that:
- If the factors are positive, the product is positive.
- If the factors have different signs the product is negative.

But what happens if both factors are negative?
need to investigate the abduction. Notes. If we subtract

(-3) five times, we can write as follows:


To calculate the product do all of these subtractions. To simplify the calculation we will add a leading zero. Remember that zero is the neutral of the sum does not affect the result.

The product of two negative numbers is a positive number!

We can summarize the cases studied in the following diagram:

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negative numbers

Monday again! And who better to start the week with a little refresher. Videito
I found these were very good and explain what work in class.
How to operations with negative numbers.

I made this video playlist at myflashfetish.com

What you think of the videos? Write a comment!
If you do not want to put your name no problem but it would be good for you to say which group you are.

REMEMBER:



NOW WITHOUT PARENTHESES
Look at the chart below and write in your notebook observe regularities, ie, what changed does not change, personal comment, etc.


notes following table now, much attention with the sign of the numbers.

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El Camino Eightfold (The Eightfold Way)


Forty years ago, in 1969, was awarded the Nobel Prize in physics Murray Gell-Mann, for his discoveries about elementary particles. If there is anything that stands in the line of discoveries and ideas of Gell-Mann is the beauty and harmony. The eightfold path eightfold way or in English, is the tip of the iceberg of the wonderful world of symmetries in particle physics.


Symmetries and conserved charges

The universe is full of symmetries that are observed by some systems. That is, there are actions which, taken on some systems, they leave their physical properties invariant. Example. Imagine a capacitor with two infinite conducting plates and parallel to each other and both perpendicular to z axis, located at z = - L, z = + L. Between them there is an electric field parallel to z axis This system has a clear translational symmetry in two directions: the two directions x, y parallel to the plates. The situation is identical in regardless of where point x, and we place ourselves.

If one imagines these two infinite plates, the system has translational symmetry in the two directions perpendicular to the z axis One of the most important physics of the last century is Noether's theorem. This tells us more or less that there is always such a burden symmetries preserved. The term load must be understood in a general context, and not just think in the electric charge for instance. In the above example, Noether's theorem tells us that two charges will be preserved one for each symmetry: one along the x axis, another along the y-axis These conserved quantities are found to be the components x, and momentum px, py.

suppose to understand between the plates put an electron. There are no forces in the plane x, y, and thus according to Newton's second law of linear momentum px, py of the electron is conserved. The shape of their movement is independent of the point in the plane x, and which is initially. Momentum is different in z (pz). Since there is an electric field in z, pz happen that will change over time according to Newton's second law. In contrast px, py are always kept constant while the electron moves between plates.

What values \u200b\u200bcan take these charges conserved? Each px, py infinite value on the real line. Whatever, this value is always constant. In short, nothing changes in the electron and its state of motion by moving it in x, y. This fact results in the conservation of momenta px, py.

Isospin and symmetry between neutron and proton


One of the bright ideas of Werner Heisenberg was to propose that there is a symmetry between proton and neutron, so that nothing changes in exchange for one another. At first glance this may seem surprising, since both have electric charges and different masses, but works with simplified physics. The mass between the two is very similar, so that Heisenberg seemed reasonable to think at first that in a universe without electromagnetic interaction the proton and the neutron would be absolutely identical - even the mass difference could be due to the electromagnetic interaction, thought.

This symmetry postulated by Heisenberg's really an expression of symmetry between the quarks that make up the proton and the neutron. These are the up and down (u, d). Its mass is very similar, but differ in electrical charge. What is this kind of symmetry between u, d? In the previous example we saw a symmetry travel in space, here is a symmetry of rotation in an internal space. In this approach or should appear simplifación therefore a conserved charge, which is known to isospin.

What values \u200b\u200bwill take charge of isospin conserved? Well, the answer to this question is one of the finest episodes of quantum theory - and whose justification is beyond the scope of this post. Mathematics show that, contrary to translational symmetry to rotational symmetries are possible discrete values. To specify a state of isospin requires two numbers. The situation is similar to the case spin. Such an electron has spin 1 / 2 and the projection of this spin on a particular axis will be +1 / 2 or -1 / 2 depending on the orientation of the electron from the axis. In the case of isospin has to be equal and both u and d are isospin 1 / 2 and the projection of this are u = +1 / 2, d = -1 / 2. As with the projection of spin, for the projection of isospin values \u200b\u200bis worth taking-I,-I +1, ... I-1, I, in steps of 1 from minus the value of isospin to the value of isospin (ie -1 / 2, +1 / 2 for isospin of 1 / 2, -1, 0, 1 for an isospin of 1).

Projection spin for a spin 1 / 2, details of the spin and the theory of rotations for example in the Wikipedia



turn the spin of the quarks is 1 / 2, both of u and the d. Unlike the spin isospin not allow us to classify in groups of two particles - that is, or in one of +1 / 2 and a -1 / 2 depending on the projection on an axis, since this projection depends on our choice of the coordinate axes - and physics is independent of them. That is, the projection of spin mixing in a single particle and is not associated with types of particles. Isospin projection, by contrast, is in an internal space symmetry where such freedom does not exist in principle.

In short, we have two quarks with two different values \u200b\u200bof the projection of isospin, and with the same spin. On the other hand, have different electrical charge. However, we have said that the electromagnetic interaction we will ignore.
Now we construct baryons, which are combinations of three quarks, with the same spin. That electric charge is equal to or not in these combinations we traro not care. Let us first consider combinations of u, d. What combinations are possible? As we have uuu, ddd, udd, uud. Of these combinations, in its ground state combinations uuu, ddd have spin 3 / 2, while that combinations udd, uud spin 1 / 2. uud and udd combinations of spin 1 / 2 correspond to the proton and neutron respectively. In these combinations as two quarks are always u and d, the value of the isospin projection of the third quark is inherited. So have isospin 1 / 2 and the projection 1 / 2 and -1 / 2 respectively.


The octet of baryons


addition to considering the quarks u, d we can also consider the s quark (strange = weird). Its mass is not as similar as those of u, d, but we can also apply to some simplification would be a symmetry between the states formed by three quarks. As we have classified the states of isospin +1 / 2 and -1 / 2 to obtain a group of two particles with very similar mass, we can classify the states of isospin + surprised (by convention strangeness -1 if the combination has a strange quark , -2 if you have two, etc..) and get a group of particles with similar masses.

As mentioned before, we distinguish between those combinations of spin 1 / 2 and those of spin 3 / 2. The same combinations of three quarks can only have spin 3 / 2. We focus on combinations of spin 1 / 2. These are as follows.

With zero s quarks: uud, udd
With

an s quark: uus, uds, dds


With two s quarks: uss, dss

What values \u200b\u200bof the projection of isospin will these combinations? In the background is clear. For example, will uss uss = +1 / 2 and dss = -1 / 2, both inherited from the value of the isospin projection of u, d, respectively. The following table shows the combinations of spin 1 / 2 with its values \u200b\u200bof isospin and strangeness, and isospin projections possible and the names of these baryons:



• Now what we do now is draw these combinations a plane with horizontal axis with the projection of isospin I3 and shaft strangeness S. vertical Get this (in this diagram are drawn also the electric charge Q and hypercharge Y):

Anyone who sees this classification for the first time this diagram can not help but wonder about the fascination of particle physics. The beauty of this classification led to its inventor, Murray Gell-Mann, to call it eightfold way, eightfold path, referring to
noble eightfold path of Buddhism. The eightfold path of Gell-Mann is the beginning of the adventure of particle physics, a story of discovery each more beautiful and profound. Other combinations


Ratings

are similar to the case of baryons with spin 3 / 2, in which case it is not a byte but a group of ten items, also for mesons (composed of a quark-antiquark pair). ratings have also been adding additional quarks and quantum numbers. That is, besides u, d, s, also consider the quarks c, b, t. Adding for example the quark c (charmed, charm) must be added a further dimension to the diagram is something like (the subíncie represents the number of c quarks in combination) - where our octet is in the database:


Differences mass start making these symmetries unsustainable and unhelpful, and also ratings over u, d, s, c, are no longer viewable.

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The number of photons of electromagnetic waves

One of the most simple and yet beautiful in the hard quantum field theory and quantum optics is that it shows that classical electromagnetic wave, as we described by Maxwell's equations must consist of an indeterminate number of photons.

The electromagnetic field can be expressed in terms of their basic modes of excitation given monent, we call photons. If the field is in a state S in which there are exactly n photons, wrote:
S = nonzero only if the field is in a superposition.

sets of photons can exist without elective and magnetic field, but they exist and oscillate in a wave, as required by Maxwell's equations, and which can act on accelerated charge, then the number of photons must be undetermined. A simple result - easy to demonstrate using creation and annihilation operators - but deep in their turn.

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The History of Number 1

's finally Friday! And spent the first week of school and begin to know a little more. I hope to complete the work they have left unfinished in class next week so I can check on the doubts. Remember

do the diagnostic test in one of the classes that are doubles.

I leave this excellent documentary, very entertaining, the History Channel. Which tells the story of numbers.
is in Portuguese, but well understood.

Have a great weekend!

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representation of numbers in a line. Class # 1

As you remember, we can represent numbers in a "number line" .

To do this properly we need:
- A point on the line called destination on which we will match the number 0 (zero)
- A unit of measure appropriate.
- a sense of growth, generally from left to right.



Thus, the numbers are split into 3 groups:
- Negatives
- Zero
- Positive
Remember that zero is neither positive nor negative.


ORDER NUMBERS Based on the above we place the numbers from 0 making the right positive and negative to the left.
The far right is a number, the greater this.


absolute value of a number. We call absolute
a number to the distance that is zero.
This amounts to consider the number NO sign.
Thus we have:
The absolute value of (+6) is 6
The absolute value of (-6) is also 6 because they are the same distance from zero. The first left and the second to the right, but the distance is the same and is equal to 6 units.


Opposite number.
opposite numbers call to have the same absolute value but opposite sign.
For example, the (-6) and (+6) are opposites. All numbers
MINUS ZERO have an opposite.

The property is opposite numbers that add up to zero.

This property is extremely useful when solving equations as we shall see.


To add signed numbers is necessary to set both the sign and the absolute value of each of the addends.

SIGNED NUMBERS ADDED
The rules are:
- To add two numbers with the same sign, add the absolute values \u200b\u200band maintaining the sign.
- To add two numbers with different signs, subtract the absolute values \u200b\u200band place the sign of the sum that has greater absolute value.

Examples:
(-4) + (-7) = (-11)
same sign (-4) + (+7) = (+3) different sign
very useful
rely on the number line to understand these rules. The following apllet
can experience. Moving

point A the first term you choose.
Then you move point B to choose the second term. The straight
below you can see the sum.



















Sorry, GeoGebra Applet can not start. Make sure you have Java 1.4.2 (or later) installed and activate JavaScript in your browser ( Click here to install Java now )








exercises.
ejercicios_01

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Assessment Regulations and grade ticket.

Rules Index:

CHAPTER I: Scope of this Regulation

CHAPTER II: initiation and completion of courses

CHAPTER III: Requirements for Admission to 1st year of CB

Chapter IV: Registration for courses regulated

CHAPTER V: inhibitions, challenges and impediments

CHAPTER VI: EVIDENCE OF STUDENT PERFORMANCE.

CHAPTER VII:

absences Chapter VIII: Special Schemes: exemptions, tolerances and other

Chapter IX: The orientation of the student's rights and duties

Chapter X: Rules to be applied at regulated students

CHAPTER XI: Rules for the passage of degree

CHAPTER XII: Teacher Meetings

CHAPTER XIII: Documenting Teacher Meetings

CHAPTER XIV: Tests and Examinations


Eval Circular 2704.

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