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The hard disk in a computer consists of an aluminum platter coated with a thin layer of a magnetic cobalt alloy. A single magnetic domain in this layer can have its magnetic moment oriented to point either parallel or antiparallel to the direction of rotation, and these two orientations can be interpreted as a binary 0 or $1 .$ Each 0 or 1 is called a bit of information. Hard disks have increased in storage capacity as new technology has decreased the physical size of the magnetic domains. Personal computer hard disks at the time this textbook was printed hold typically 250 gigabytes (GB) of data, where each byte contains 8 bits. A standard hard-disk platter is $9.5 \mathrm{cm}$ in diameter and has a 2.5 -cm-diameter hole in the center for mounting it on the drive. Bstimate the edge length of a magnetic domain on a computer Bstimate the edge length of a magnetic domain on a computer hard disk, assuming them to be square.

This question refers back to the process of making amino acid residues from code ons. Now in this specific question were given that a C. A poli poli code on is given. So we have a continuous C A C A C A. And this will give two amino acid rescues. It will give both reunion and history. Now the code ons that are used to the in the process of making these two recipes is see A C and A C. A. And as we can see on the polly code on sequence, there's C. A C. And how a CIA can also be read. So we have to figure it out which one of these two code arms Will be the code on four to your reunion And which one will be the code on for history. Now to solve this, were given another piece of information, an artificial M R N A. Again, also a poli code on sequence. This one is going to be C A C A C A. And continuously since. Since since it's an artificial M. RNA. You can also be read in different directions and were given that it could also read a C. A C. A. Or it could also read a A C A a C. Continuously. So we will have three types of readings from that artificial Mariana. And these three types of readings will give, well three poly change of recipes. The first one we pull you through union, second we poorly glutamine and the third one we bloody a spur. Again. Now we noticed that the second one also codes for a three union which is which correlates to our first one. Which is part of our question. Also we have to notice that A C. A. Is a code on that also matches a C. A. From the first question since the re owning is the only rest of you That also matches The 1st 1, then A. C. A. Must be the code on 4th reunion, and thus C A C must be coming for history. And this is how we solved for the currents of each of universal recipe.

In 1 10 It's about a dinosaur, and as it grows, its crest increases in length from 1.5 meters to 2.7 meters. Remember, the crest is the thing on its head that resonates sound like an open pipe. So as a length increases office flee, the frequency would go down and it would go down for the fundamental and the second harmonic and the third harmonic. They would all go down. But this question ask the change in frequency for the fundamental would that be greater than less than or equal to the change for the second hormone. So if you look on the table, we're supposed to refer to the figure 14-54 if you look at it for those for those legs local 1.5 22.7. If I look for the fundamental frequency which is this and compare that to the second harmonic, which is this Look at this change, you know it's going from like here. Here were As for the second harmonic at 1.522 point seven, that is definitely a bigger change, you know, look at the change in Y on this This definitely has a bigger change than that does. So when it asked, So the change for the fundamental frequency would be less than the change for the second harmonic.

In this example, we have a consumption matric see which provide is provided here and this is a seven by seven matrix of the United States economy as it was in 1958. So what we have here next is a particular demand factor. This vector D is given to be first 74,000 then 56,000. For the third sector of the economy, we have 10,500 for the fourth sector, we have 25,000. The next sector is 17,500. Next we have 196 100,000 and the final is 5000 from the seventh sector. So the units here are in millions of dollars. And the long Tom Fif model for this particular situation is of the form, see or rather, I minus c times the production Vector X, which is are unknown, which is equal to the demand vector d. So we consult this, but what we would need to do is form a new matrix, which is going to be C minus. I augmented with the demand vector d. This takes quite a while to compute such a matrix. Even if it's just working out to this portion. Hope and it should be I minus c here. Not a C minus I, but putting this into a computer algebra system. We see that this is equal to this rather large matrix that we see here. So informing that matrix I took, I dont matrix that we see here we went to the main diagonal. It took one minus all of these entries. So, for example, in this entry, one mice 10.12 gives us the 0.9988 then the remainder entries in the and the consumption matrix C We just took the opposites. That's why you see all these negative signs and that gives us I minus c. Then here we have a augmented with the vector d. What we need to do next is ro reduce this entire seven by eight matrix, but this is not something that should be done by humans. So let's put this back into the computer algebra system and roll reduce. So, in my computer algebra system, I found that this matrix is row equivalent to this monstrosity we see below. But don't forget that we have augmented. Oh, dear. That was a wrong matrix. It's Rocca linked to this matrix we see displayed here. We have ones on the main Dagnall going this way, which tells us that our consumption matrix see when we for my my a c we did get a convertible matrix. Now this column here tells us that the production level X that's required is X equals 99,575 0.7 and these are in units of millions of dollars from the first sector of the economy. Then it's 97,000 703. 51,230 0.5 from the third sector, then 131,570 49,000 488 0.5, then 329,000 554. And lastly, 13,000 835.4 from the last sector of the economy. So this vector X is the production vector required, given the consumption matrix and the demand vector

In number 108 We're told that the female dinosaur has a shorter crest than the male and were asked if their fundamental frequency of the sound she makes will be, um, greater less than or the same as the mail. So that crest, remember, That's the thing on the head that acts like a resonating to. So if it has a shorter crest, that means it's gonna have a shorter wavelengths. And if I remember how wavelength is relayed to frequency, um, the speed's not gonna change that speed of sound. So if the wavelength is going down, the frequency must be going up so she would have a greater frequency. So just like humans, the girl dinosaurs would have a higher voice.


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