master of your domain
where’s the beef?
every home should have one!
if anything can go wrong, it will
never mind
don’t worry, be happy
after all, tomorrow is another day
give me a hug
It’s good to talk
Michael Artin's Algebra Exercises
1 Matrices
Section 1 The Basic Operations
1.1. What are the entries \( a_{21} \), and \( a_{23} \) of the matrix A = \( \begin{bmatrix}
1 &2 &5 \\
2 &7 &8 \\
0 &9 &4
\end{bmatrix} \) ?
\( a_{21} = 2 \), and \( a_{23} = 8 \)
1.2. Determine the products AB and BA for the following values of A and B:
\( A = \begin{bmatrix}
1 &2 &3 \\
3 &3 &1
\end{bmatrix}, \hspace{2mm}
B = \begin{bmatrix}
-8 &-4 \\
9 &5 \\
-3 &-2
\end{bmatrix} \)
\( AB = \begin{bmatrix}
1 &0 \\
0 &1
\end{bmatrix}, \hspace{4mm}
BA = \begin{bmatrix}
-20 &-28 &-28 \\
24 &33 &32 \\
-9 &-12 &-11
\end{bmatrix} \)
\(
A = \begin{bmatrix}
1 &4 \\
1 &2
\end{bmatrix}, \hspace{2mm}
B = \begin{bmatrix}
6 &-4 \\
3 &2
\end{bmatrix}
\)
\( AB = \begin{bmatrix}
18 &4 \\
12 &0
\end{bmatrix}, \hspace{4mm}
BA = \begin{bmatrix}
2 &16 \\
5 &16
\end{bmatrix} \)
1.4. Verify the associative law for the matrix product
\( ABC = \begin{bmatrix}
1 &2 \\
0 &1
\end{bmatrix}
\begin{bmatrix}
0 &1 &2 \\
1 &1 &3
\end{bmatrix}
\begin{bmatrix}
1 \\
4 \\
3
\end{bmatrix} \)
Note: This is a self-checkingproblem.It won’t come out unless you multiply correctly. If you need to practice matrix multiplication, use this problem as a model.
\( (AB)C = \begin{bmatrix}
2 &3 &8 \\
1 &1 &3
\end{bmatrix}
\begin{bmatrix}
1 \\
4 \\
3
\end{bmatrix}
= \begin{bmatrix}
38 \\
14
\end{bmatrix}
= 2 \begin{bmatrix}
19 \\
7
\end{bmatrix}
\)
\( A(BC) = \begin{bmatrix}
1 &2 \\
0 &1
\end{bmatrix}
\begin{bmatrix}
10 \\
14
\end{bmatrix}
= \begin{bmatrix}
38 \\
14
\end{bmatrix}
= 2 \begin{bmatrix}
19 \\
7
\end{bmatrix}
\)
Proverbs
Far from eye, far from heart.
Friends agree best at a distance.
Out of sight, out of mind.
Long absent, soon forgotten.
Nothing seek, nothing find.
Anger punishes itself.
A hungry man is an angry man.
Fear of death is worse than death itself.
He laughs best who laughs last.
The unexpected always happens.
Never judge from apperances.
Better to ask the way than go astray.
Like question, like answer.
It is not every question that deserves an answer.
Every beginning is hard.
Such beginning, such end.
Nurture is above nature.
Nurture and good manners maketh man.
Manners and money make a gentleman.
‘After you’ is good manners.
Curiosity is ill manners in another house.
Better the devil you know than the devil you don’t know.
There is nothing permannent except change.
There is nothing new under the sun.
The apple never falls far from the tree.
Boys will be men.
You pays your money and you takes your choice.
The customer is always right.
Content is happiness.
A little bird is content with a little nest.
刻几何原本序
唐、虞之世，自羲、和治曆，暨司空、后稷、工、虞、典乐五官者，非度数不为功。《周官》六艺，数与居一焉；而五艺者，不以度数从事，亦不得工也。襄、旷之于音，般、墨之于械，岂有他谬巧哉？精于用法尔已。故尝谓三代而上，为此业者盛，有元元本本、师傅曹习之学，而毕丧于祖龙之焰。汉以来，多任意揣摩，如盲人射的，虚发无效；或依拟形似，如持萤烛象，得首失尾。至于今而此道尽废，有不得不废者矣。
《几何原本》者，度数之宗，所以穷方圆平直之情，尽规矩准绳之用也。利先生从少年时，论道之暇，留意艺学，且此业在彼中所谓师傅曹习者，其师丁氏，又绝代名家也，以故极精其说。而与不佞游久，讲谈余晷，时时及之。因请其象数诸书，更以华文。独谓此书未译，则他书俱不可得论，遂共翻其要约六卷，既卒业而复之，由显入微，从疑得信。盖不用为用，众用所基，真可谓万象之形囿，百家之学海。虽实未竟，然以当他书，既可得而论矣。
私心自谓，不意古学废绝二千年后，顿获补缀唐、虞、三代之阙典遗义，其裨益当世，定复不小。因偕二三同志，刻而传之。
先生曰：「是书也，以当百家之用，庶几有羲、和、般、墨其人乎，犹其小者，有大用于此，将以习人之灵才，令细而确也。」余以谓小用大用，实在其人。如邓林伐材，栋梁榱桷，恣所取之耳。顾惟先生之学，略有三种，大者修身事天，小者格物穷理。物理之一端，别为象数，一一皆精实典要，洞无可疑，其分解擘析，亦能使人无疑。而余乃亟传其小者，趋欲先其易使人绎其文，想见其意理，而知先生之学可信不疑。大概如是，则是书之为用更大矣。他所说几何诸家，藉此为用，略具其自叙中，不备论。
吴淞徐光启书。
My English Phrases List - November - 2025
get a move on
You’d better get a move on, darling. If you don’t hurry you’ll miss the train.
Could you get a move on?
She told her partner to get a move on or they would be late.
the other day/night/morning/afternoon/evening
on a day/night/morning/afternoon/evening in the recent past
The other morning, I saw a deer on our lawn.
backseat driver
bed head
He is a small man with a salt-and-pepper beard, very bright brown eyes and a perpetual case of bed head, little tufts flying every which way.— Alex Witchel
city slicker
city slickers who’ve never seen a real farm
party pooper
Don’t be such a party pooper!
a party pooper who insisted they turn the music down
tear down
Tear down this wall! - Ronald Reagan
treble clef
- a clef that places G above middle C on the second line of the staff
bass clef
- a clef placing the F below middle C on the fourth line of the staff
My English Words List - November - 2025
baguette
noun
On a first-time trip to Paris, biting into the city’s best baguettes and croissants is as much on the bucket list for many as a visit to the Eiffel Tower or Louvre. — Lane Nieset, Travel + Leisure, 5 Oct. 2025
kinsman
noun
A near neighbour is better than a far-dwelling kinsman.
broom
noun
A new broom sweeps clean.
groom
noun
copycat
noun
She called me a copycat for wearing the same dress.
provoke
verb
The animal will not attack unless it is provoked.
Prime Minister Mark Carney says he advised Premier Doug Ford against running the anti-tariff ad campaign that provoked U.S. President Donald Trump and spurred him to break off trade negotiations. — Waterloo Region Record, November 3, 2025
bumpkin
noun
We enjoyed living a kind of country bumpkin way of life.
killjoy
noun
his perpetually negative attitude made him a real killjoy when others were trying to have fun
homebody
noun
He’s a homebody who hates parties.
nitpick
verb
My mom would nitpick everything about me, from my hair to my etiquette. — Bon Appétit, 14 May 2021
demolish
verb
The old factory was demolished to make way for a new parking lot.
foliage
noun
trees with colorful autumn foliage
Fall foliage experience is a feast for the eyes.
psychosis
noun
Cannabis users now develop psychosis at five times the rate of non-users. — Joseph Epstein, Newsweek, 10 Dec. 2024
veteran
noun
Veterans’ Week and Remembrance Day
Canada’s oldest veteran turns 110 on Remembrance Day week.
staff
noun
- the horizontal lines with their spaces on which music is written
itch
verb
This sweater makes me itch.
noun
I had a slight itch on my back.
Quotes
© selected from 1001 Quotations To Enlighten, Entertain, and Inspire, by Robert Arp
One man’s meat is another man’s poison. - Lucretius
Death comes equally to us all, and makes us all equal when it comes. - John Donne
The way to get started is to quit talking and begin doing. - Walt Disney
Yesterday is gone. Tomorrow has not yet come. We have only today. Let us begin. - Mother Teresa
Kindness in words creates confidence. Kindness in thinking creates profoundness. Kindness in giving creates love. - Laozi
The possession of a book becomes a substitute for reading it. - Anthony Burgess
You can never plan the future by the past. - Edmund Burke
Let us learn from the past to profit by the present, and from the present to live better in the future. - William Wordsworth
That sign of old age: extolling the past at the expense of the present. - Sydney Smith
I realise that patriotism is not enough. I must have no bitterness or hatred towards any one. - Edith Cavell
In the moment of crisis, the wise build bridges and the foolish build dams. - Nigerian Proverb
Man differs more from man, than man from beast. - John Wilmot, Earl of Rochester
Birth is suffering, aging is suffering, illness is suffering, death is suffering. - Buddha
If at first you don’t succeed, try, try, try again. - Thomas H. Palmer
Remember that time is money. - Benjamin Franklin
Business? It’s quite simple. It’s other people’s money. - Alexandre Dumas the Younger
A business that makes nothing but money is a poor business. - Henry Ford
Society cares for the individual only so far as he is profitable. - Simone de Beauvioir
There is only one boss. The customer. And he can fire everybody in the company from the chairman on down, simply by spending his money somewhere else. - Sam Walton
Man is a tool-using animal … Without tool he is nothing, with tool he is all. - Thomas Carlyle
Technology is useful servant but a dangerous master. - Christian Lous Lange
Any sufficiently advanced technology is indistinguishable from magic. - Arthur C. Clarke
The important thing to remember is that the Internet is not a new form of life. It is just a new activity. - Esther Dyson
Chance favors only the prepared mind. - Louis Pasteur
Art is I; science is we. - Claude Bernard
Basic research is what I am doing when I don’t know what I am doing. - Wernher von Braun
God used beautiful mathematics in creating the world. - Paul Dirac
The most important thing in the Olympic Games is not to win, but to take part. - Pierre Frédy, Baron de Coubertin
One man practicing sportsmanship is far better than a hundred teaching it. - Knute Rockne
Dream as if you’ll live forever. Live as if you’ll die today. - James Dean
Everything will pass, and the world will perish, but the Ninth Symphony will remain. - Mikhail Bakunin
Continue to play Bach your way and I, his way. - Wanda Landowska
My English Phrases List - October - 2025
honesty is the best policy
idiom
He realized honesty is the best policy and told them what really happened to their car.
as old as the hills
idiom
So this message, that good, close relationships are good for our health and well-being, this is wisdom that’s as old as the hills. Why is this so hard to get and so easy to ignore? Well, we’re human. What we’d really like is a quick fix, something we can get that’ll make our lives good and keep them that way. Relationships are messy and they’re complicated and the hard work of tending to family and friends, it’s not sexy or glamorous. It’s also lifelong. It never ends. - What makes a good life? Lessons from the longest study on happiness, by Robert Waldinger
(as) blind as a bat
idiom
Without glasses I’m blind as a bat.
I’m as blind as a bat without my glasses.
People in the U.S. use the phrase “blind as a bat” to rib someone for not being able to see well. - Myth Busting ‘Blind As A Bat’ And ‘Memory Of A Goldfish’
memory of a goldfish
There is a myth that goldfish have a memory of only three seconds.
For years, people have used: “You’ve got a memory like a goldfish,” as an insult, based on the misconception that they have a very short memory span. Actually, it’s a compliment. - Memory like a goldfish? Why this could be a good thing
Memory of a goldfish? Maybe you’re not so forgetful after all.
as deaf as a post
idiom
My grandmother’s a sweet old lady, but she’s as deaf as a post.
as good as gold
his promise is as good as gold
the child was as good as gold
The children were as good as gold while they stayed with their grandmother.
like the wind
idiom
We had to run like the wind to catch the bus!
as quiet as a mouse
idiom
In addition to being sophisticated, this appliance is both Energy Star and NSF certified, is as quiet as a mouse, and can both wash and dry dishes. — Kat De Naoum, Better Homes & Gardens, 4 Oct. 2023
Paul is as quiet as a mouse. He never talks in meetings.
(as) big as life
I never expected her to come to the party, but there she was, as big as life.
People big as life, bright as day everywhere in this house. — Andrew Cockburn, Harper’s Magazine, 20 Aug. 2024
as busy as a bee
idiom
She’s as busy as a bee.
as clear as day/daylight/anything
idiom
The sign said/read “Keep Out” as clear as day/daylight/anything.
(as) pretty as a picture
And just like that, your living room can be as pretty as a picture. — Elise Taylor, Vogue, 19 Feb. 2021
(as) clear as a bell
Clear as a bell, I heard him say my name.
It was clear as a bell that morning—not a cloud in the sky.
The water was as clear as a bell.
a picture is worth a thousand words
idiom, Proverbs
As the saying goes, a picture is worth a thousand words. — Megan Poinski, Forbes.com, 2 July 2025
Just as a picture is worth a thousand words, a meme is worth a thousand tweets. — Ernesto Verdeja, The Conversation, 24 Apr. 2025
If a picture is worth a thousand words, then how much is a video worth? — Kristen Moon, Forbes, 19 Oct. 2024
(it’s) better (to be) safe than sorry
It’s probably not necessary to check the figures again, but it’s better to be safe than sorry.
So, for your well-being and pocketbook, better to be safe than sorry. — USA TODAY, 14 Jan. 2024
beauty is in the eye of the beholder
The clichés and the sayings about beauty are usually true, like how people say that beauty is in the eye of the beholder. — Kate Erbland, IndieWire, 19 Mar. 2025
Just as beauty is in the eye of the beholder, meaning is in the mind of the interpreter. — Dr. Marcus Collins, Forbes, 14 Oct. 2024
a watched pot never boils
Stop sitting by the phone waiting to hear if you got the job. A watched pot never boils.
there’s no time like the present
“Should we do it now?” “Sure. There’s no time like the present.”
Stop complaining about your toothache and call the dentist. There’s no time like the present.
And there’s no time like the present to get it at the lowest possible price. — Jake Smith, Glamour, 27 Nov. 2023
a penny saved (is a penny earned)
Another study found that about 40% of Gen Xers don’t have a penny saved for retirement. — Aimee Picchi, CBS News, 17 Dec. 2024
two heads are better than one
idiom
We need to work together to figure this out. Two heads are better than one.
eat crow
He was forced to eat crow when the company fired him.
Tesla would have to eat a lot of crow to change their mind on this, but what better way to eat crow than to do it in a splash announcement. — Brad Templeton, Forbes, 7 Oct. 2024
He wanted to make his critics eat crow.
the so-called experts will be eating crow tonight.
eat humble pie
They had to eat humble pie when the rumors they were spreading were proved false.
After boasting that his company could outperform the industry’s best, he’s been forced to eat humble pie.
Anson was forced to eat humble pie and publicly apologise to her.
My English Words List - October - 2025
sunset
noun
We worked from sunrise to sunset.
the golden light of sunset
A young man sees a sunset and, unable to understand or to express the emotion that it rouses in him, concludes that it must be the gateway to world that lies beyond. - The catches of life, Pieces of Mind, by C. E. M. Joad
subset
noun
the set of even numbers is a subset of the set of all numbers
a subset of our community
gibbous
adjective
The waxing gibbous moon provided the perfect lighting for a night of spooky storytelling around the campfire.
At 3:30 a.m. the gibbous moon is high in the south and Perseus is nearly overhead. Set up a comfortable lawn chair facing away from any bright lights, ideally looking toward the northeast with the moon to your back. Have insect repellent handy along with hot chocolate, tea or coffee and enjoy the show. — Tim Hunter, The Arizona Daily Star, 7 Aug. 2025
ignite
verb
The fire was ignited by sparks.
a material that ignites easily
vent
noun
revelation
noun
Sunlight, for instance, often stands in for divine grace or revelation.
We simply must rely on God to give us divine revelation by his Holy Spirit.
fuddy-duddy
noun
They think I’m an old fuddy-duddy because I don’t approve of tattoos.
prank
noun
He enjoys playing pranks on his friends.
as a prank, several students managed to change all the classroom clocks to different times
First reaction of Michel Devoret, 2025 Physics Nobel laureate: ‘I thought it was a prank. The quantum computer is not here yet’
mogul
noun
Hollywood moguls
industry moguls
Trump has already hinted at some names, including Oracle co-founder Larry Ellison, billionaire tech investor Michael Dell, businessman and media mogul Rupert Murdoch, and his son Lachlan Murdoch. — James Powel, USA Today, 7 Oct. 2025
Larry Ellison, the 81-year-old tech billionaire-turned-media mogul.
chiropractic
noun
Some mainstream doctors may view it as a fringe treatment, but chiropractic is more commonly covered by insurance than any other type of alternative care.— Elizabeth R. Agnvall
adjective
Chiropractic treatment involves manual spinal adjustments to unblock the flow of energy and blood to the nervous system; it can also include nutritional counseling and stress management. — Corynne Corbett
boo-boo
noun
- a usually trivial injury (such as a bruise or scratch)
— used especially by or of a child
When Cody trips and falls in the grass, his friends band together to comfort him and get him a bandage for his boo-boo. — Elisabeth Sherman, Parents, 9 May 2025
nasty
adjective
nasty living conditions
a nasty taste
living a cheap and nasty life — G. B. Shaw
She has a nasty habit of biting her fingernails.
That nasty old man yelled at me just for stepping on his lawn!
orator
noun
Jeff Dean was a world-class engineer, not an orator. - Genius Makers, The Mavericks Who Brought AI to Google, Facebook, and the World, Cade Metz
ponytail
noun
She usually wears her hair pulled back in a ponytail.
In the United states, connectionist research nearly vanished from the top universities. The one serious lab was at New York University, where Yann Lecun took a professorship in 2003, his hair pulled back in a ponytail. - Genius Makers, The Mavericks Who Brought AI to Google, Facebook, and the World, Cade Metz
bail
noun
Prime Minister Mark Carney says his Liberal government will introduce legislation next week to crack down on crime by bringing in harsher sentencing and making bail much harder to get.
tact
noun
questions showing a lack of tact
Tact is the art of making a point without making an enemy. - Isaac Newton
The ability to show tact has been emphasized since the earliest proverbs, including this one from the Bible:”A gentle answer turns away wrath, but a harsh word stirs up anger.“ - 1001 Quotations To Enlighten, Entertain, and Inspire, by Robert Arp
bloom
noun
the spring bloom
the roses are in bloom
the rosebush produces blooms only in midsummer
a handsome young man in the full bloom of youth
That is why I never employ an expert in full bloom. - Henry Ford
My English Phrases List - September - 2025
How are you?
American English
Very common, often just a polite greeting, not always expecting a detailed answer.
Typical reply: “Good, thanks. How about you?” (even if not really “good”).
Tone is casual and friendly.
Canadian English
Used the same way as in American English.
Canadians might also add extra politeness: “Good, thanks! And yourself?”
Sometimes paired with “Hi there” or “Hey” for warmth.
British English
Also common, but sometimes interpreted more literally.
You might hear “Not bad, thanks” or “I’m alright” more often than “Good”.
Can sound slightly more formal than in North America, depending on context.
How do you do?
American English
Rare, sounds very formal or old-fashioned.
Most Americans would never use it in daily conversation.
Canadian English
Similar to American usage — hardly used except in very formal, ceremonial, or joking contexts.
British English
Still exists in formal settings (business introductions, very polite first meetings).
Important: it’s not really a question — it’s a formal greeting.
Standard reply: “How do you do?” (you repeat it back, rather than answering literally).
talk the talk
Sure, she talks the talk, but can she walk the walk? Will she actually do what she promises?
walk the walk
As the saying goes, “Don’t talk the talk unless you can walk the walk!”
pie in the sky
Is that even possible, or is that ‘pie in the sky’ thinking? — Rachel Wells, Forbes, 1 Jan. 2025
meet one’s Waterloo
The governor finally met his Waterloo in the last election.