a year ago

If you transported back in time in middle ages, and the king asks you to show off your amazing knowledge and useful skills from the future - what would you do to impress people?

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of course I will tell you about developments in advanced technology, such as internet networks that are now easily accessible anywhere, because the internet is a network that makes communication and information especially much easier than the century of development
Depends on what you can bring with you, if it's just what's in your head... I think I could make gunpowder.

Without props it would actually be pretty difficult to convince the you weren't damaged in the head as your speech would be so different they wouldn't even understand you.
"This would be long "

The whole premise of the original unedited form of the question* is based on misunderstanding of how technology and science were seen in the Middle Ages. Firstly, people who introduced innovations in science and technology were not "burned at the stake" in the Middle Ages - that is a Nineteenth Century myth. On the contrary, they were lauded and celebrated. Those universities mentioned in the question, institutions of learning and inquiry given to the world BY the Medieval Era, were established and run by an intellectual elite that loved new knowledge, revived lost learning and embraced new ideas. So why would they "burn at the stake" someone who came to them with science and innovation?

In the mid Twelth Century the English scholar Daniel of Morley studied first at Oxford University and then at Paris, but was dissatisfied with what he was learning there when he heard that more innovative and advanced knowledge could be found elsewhere:

I heard that the doctrine of the Arabs, which is devoted almost entirely to the quadrivium, was all the fashion in Toledo in those days, I hurried there as quickly as I could, so that I could hear the wisest philosophers of the world … 

The "quadrivium" he mentions were the four advanced "arts" of arithmatic, geometry, music and astronomy, though he he is referring to more advanced knowledge generally, including logic and "natural philosophy" or what we call science. And did Daniel's contemporaries condemn him or threaten to burn him at the stake for seeking out advanced knowledge or science? No, they begged him to come back to England and share it with them:

Eventually my friends begged me to come back from Spain; so, on their 
invitation, I arrived in England, bringing a precious multitude of books
 with me. 

Daniel of Morley was only one scholar in this period who learned "the doctrine of the Arabs" and brought back a treasure trove of books of science and philosophy not just by Arab and Jewish scholars but also lost works by ancient Greek writers like Aristotle, Plato, Archimedes and Ptolemy. While in Spain he met many other scholars from across Europe who were there, learning Arabic and Hebrew and studying with Muslim and Jewish scholars for the same purpose. One was an Italian, Gerard of Cremona, who had come to Spain specifically to find one major lost book of astronomy and who later returned to Italy having translated no less than 87 major works of science and philosophy into Latin. Gerard exalted reason above all else. He once wrote to a rival:

I have learnt one thing from my Arab masters, with reason as guide, but you another: you follow a halter, being enthralled by the picture of authority. For what else can authority be called other than a halter?

Gerard was also not "burned at the stake" and died one of the most revered and exalted scholars in Europe.

And would telling people about amazing technical innovations get you "burned at the stake"? No, it wouldn't. The Middle Ages was a period in which people embraced technical innovation as never before. It was actually the first period in European history when people really began to harness the power of machines and where innovations in mechanical power were embraced:

The Middle Ages introduced machinery into Europe on a scale no civilization had previously known. This was to be one of the main factors that led the the dominance of the Western hemisphere over the rest of the world.
(Jean Gimpel, The Medieval Machine: The Industrial Revolution of the Middle Ages, p. 1)

And we have an example of someone talking to Medieval scholars about remarkable "scientific discoveries and technological wonders". In 1250 the great Medieval scholar and scientist Roger Bacon did just that, talking about mechanical ships, vehicles driven by their own power and flying machines:

By the figurations of art there have been made instruments of navigation without men to row them, as great ships to navigate the sea, only with one man to steer them, and they sail far more swiftly than if they were full of men; also vehicles that shall move with unspeakable force without any living creature to stir them. Likewise an machine may be made to fly as one sits in the midst of the instrument and turns an engine, by which the wings, being artificially composed, beat the air after the manner of a flying bird.
(Roger Bacon, "Epistola de secretis operibus")

Bacon is also the first European writer to tell his fellow scholars of a new innovation from the east, an explosive powder which is produces "hideous cracklings" and which can destroy armies - gunpowder.

Was Bacon "burned at the stake" or threatened for talking about these technological marvels? No, he was lauded for his scholarship and learning and dubbed "Doctor Mirabilis" - the miraculous doctor.

The question above is based on a Nineteenth Century misunderstanding about the Middle Ages, which in turn was based on a ignorance of the period and prejudice against it. We now have a much better understanding of how Medieval people saw the world and have begun to reassess it as a period of great intellectual curiosity and the beginings of European scientific and technical innovation, not a dark age at all.

* The original question assumed anyone who talked about new learning and technological marvels to Medieval scholars would be imminent danger of being "burned at the stake" and so would have to prove they were not some kind of heretic. My answer doesn't make much sense given that the question has now been edited to remove this misunderstanding about the Middle Ages.Us
Electricity - would be a huge game changer for them
I teach them how to make chocolate
Make simple Python programs to make their life more simple and easy ,.... But first i have to build a computer and everything ...
show them mobile phone,
Just use map online or Google location on the phone and tell the best location to go.
His mom
Just show them a phone